The nation's governors concluded a quiet conference in Washington yesterday with warm praise for President Carter, requests for additional financial aid from Congress and a last-minute denunciation of foreign-flag tankers that pollute American waters.

The tanker issue, one of the few that provoked any debate at the annual midwinter meeting in Washington, arose when Gov. Milton J. Shapp (D-Pa.) offered an amendment to a resolution supporting "rigorous standards for the construction and operation of oil tankers and for the training and licensing of their officers, crews and pilots."

Shapp's amendment called for foreign flag tankers, such as the Liberian tanker Argo Merchant, which ran aground off Nantucket last Dec. 15, to meet the same safety standards as U.S. ships.

Gov. Pierre S. du Pont IV (R-Del.) objected that this would abrogate six international treaties and be "a serious mistake."

"We would much rather destroy six international treaties than the beaches of New Jersey," responded Gov. Brendan T. Byrne (D-N.J.)

The amendment and resolution passed on a divided voice vote. Most of the other resolutions at the conference were approved unanimously, except for an endorsement of a pending stripmining bill, which was supported by all governors except George C. Wallace (D-Ala.) and Dolph Briscoe (D-Tex.)

The resolutions for the most part expressed fimiliar positions of the National Governors Conference calling for more federal funding and less federal red tape. The governors ducked a number of the tougher issues before Congress, such as the question of auto emission standards in the Clean Air Act, which the governors said the auto industry should meet "as expeditiously as is practical."

The conference's natural resources panel deleted a staff recommendation calling for a tougher statement on the auto emission issue. Midwestern governors, led by William G. Milliken (R-Mich.), said the auto industry might not be able to produce 1978 models if auto exhaust standards are too stringent.

The governors called for a number of actions by Congress, including combining of 53 Medicaid programs into "a single organizational entity." They also urged Congress to create a new youth unemployment program and appropriate $1.8 billion to fund it.

Congressional leaders treated the governors to a steak lunch on Capitol Hill yesterday, but offered them nothing substantial in the way of federal funding. A number of governors want more federal aid to deal with the effects of the winter and the Western drought.

The pattern of courteous treatment combined with an absence of any specific promises was the pattern during the three-day midwinter conference, which concluded last night with a black tie dinner at the White House for the governors and their spouses.

The 47 governors who attended the meeting, including many of the 12 Republicans, seemed particularly impressed with the attention given them by President Carter.

Milliken was chosen by his fellow GOP governors as the next chairman of the National Governors Conference, a post that is rotated between the parties. Gov. Patrick J. Lucey of Wisconsin was elected chairman of the Democratic governors.