Profits of the Washington Post Co. declined 5 percent last year but were 17 percent higher during the final quarter of the year than in 1980, while Gannett Co. profits rose 14 percent in the latest three months and in the full year, the communications companies reported yesterday.

Separate reports from other newspaper publishers and media firms--including Dow Jones & Co., Capital Cities Communications, Media General Inc. and Knight-Ridder--indicate that the fourth quarter of 1981 generally was weaker for these businesses than had been forecast earlier in the year as recession ate into advertising volume and record interest added to costs.

The Post Co., which owns Newsweek magazine, four television stations, The Post newspaper here and the Everett (Wash.) Herald, said overall profits in 1981 decreased to $32.7 million ($2.32 a share) from $34.3 million ($2.44) the previous year, as revenues rose 14 percent to $753 million. The profits were lower by $2.1 million (15 cents) because of losses associated primarily with the Trenton, N.J., Times, which was sold last fall to D.C. financier Joe L. Allbritton.

Post Co. operations also were affected dramatically by the decision last summer of Time Inc. to close its money-losing Washington Star. Circulation of the daily Post jumped more than 20 percent in a short period of time, and production costs soared.

In the wake of the new circulation figures, The Post raised advertising rates last fall and is moving to boost ad rates in the near future, newspaper President Thomas Ferguson said yesterday. Home-delivery circulation prices of the paper also were raised recently, for the first time in two years.

In the fourth quarter alone, Post Co. profits were "a bit better" than had been expected, according to the company's vice president for finance, Martin Cohen. Profits rose to $18.1 million ($1.28) from $15.4 million ($1.10) as revenues jumped 18 percent to $218 million. About 7 cents per share of the quarterly gain reflected the sale of Inside Sports magazine--which didn't take place formally until 1982, but which was negotiated before the end of 1981.

Gannett Co., a Rochester, N.Y., company that owns the nation's biggest newspaper chain, said profits for 1981 were $172.5 million ($3.17 a share) compared with $152 million ($2.81) in 1980, while revenues expanded 13 percent to $1.37 billion. Fourth-quarter net totaled $54.6 million ($1.01) compared with $47.9 million (88 cents), as revenues rose 12 percent to $377 million.

For Gannett, it was the 14th consecutive year of record earnings and revenue gains--a string that may come to an end this year because of start-up costs for the firm's new Washington-based national daily newspaper, USA Today, scheduled to begin publication next fall.

Company Chairman Allen Neuharth forecast yesterday that while annual earnings can continue to grow over the next couple of years, the rate of profit increases is projected to be somewhat lower than Gannett's 14-year average.

"After that, however, these annual earnings gains are projected to be sharply higher," he added.

Industry analyst Bruce Thorp, in the Washington office of Lynch, Jones & Ryan, said yesterday that Post Co. and Gannett earnings were about in line with his firm's forecasts, although Wall Street analysts interviewed by Barron's magazine for its Feb. 1 issue had estimated Post Co. annual earnings for 1981 at $2.05-$2.20 or lower, compared with the $2.32 reported yesterday.

A Post Co. statement attributed the improved fourth quarter mainly to increased revenue at The Post newspaper. "Although manufacturing and distribution expenses were up substantially due to the circulation added since the Washington Star ceased publication in August, increased advertising volume resulted in higher operating pretax profit," the company stated.

In the third quarter, profits from The Post newspaper had declined because of the costs associated with a sudden increase in circulation, purchase of The Star's old plant and equipment, and additions to the publication's staff. As of Dec. 31, according to figures submitted to the Audit Bureau of Circulation, Post daily circulation was up 146,000, or 23 percent, to 770,500, while Sunday circulation spurted 141,000, or 17 percent, to 984,000 compared with the same figures a year earlier.

Post President Ferguson noted that a 10 percent increase last October in retail and classified advertising rates had not matched the readership gains or higher costs. He said Post executives are studying a new retail-classified ad rate boost between 10 percent and 15 percent, probably to take effect April 1; a 12 percent ad rate increase was initiated last April, before The Star's closing.

On Jan. 25, The Post increased to $8 from $7 the home-delivered price of the newspaper every four weeks.

During 1981, the Post Co.'s newspaper division listed an 18 percent increase in revenues and a 4 percent decline in pretax profits, with ad linage in The Post up 4 percent. Broadcasting revenues rose 13 percent, but operating profits fell 5 percent because of an increase of $2.3 million on program production activity. Magazine division operating profits rose 21 percent on a 10 percent increase in revenues, with the higher profitability attributed primarily to reduced losses at Inside Sports, a publication started in 1981.

In January, Active Markets Inc., of Bellevue, Wash., purchased Inside Sports for at least several million dollars, although both companies have declined to give a specific price.

Among other communications companies reporting:

Capital Cities Communications Inc., owner of the Kansas City Star and Times and other newspapers, broadcast and cable TV operations, said profits rose to $80.5 million ($6.12 a share) from $70.8 million ($5.38), as revenues increased to $574 million from $472 million. Fourth-quarter net income was $22.4 million ($1.70) vs. $20 million ($1.52).

Dow Jones & Co., publisher of The Wall Street Journal, Ottaway newspapers and Barron's, said profits rose 21 percent in 1981 to $71.4 million ($2.28 a share) from $58.9 million ($1.89) as sales climbed 21 percent to $641 million. Ad linage in the Journal was up 10 percent; circulation rose 3.6 percent to 2 million.