The last-minute hitch in releasing the American hostages in Beirut today was in some ways perhaps more embarrassing to Syria than to the Reagan administration.

For the first time in recent memory the proverbially prudent Syrian government threw caution to the winds and published a series of statements assuming that the hostages had been freed and were on their way by road to Damascus.

That was at midday. Everything here in the Syrian capital then appeared to be going according to the schedule first disclosed shortly after 2 a.m. (7 p.m. EDT Friday) when Information Ministry officials awakened television crews to say the hostages would arrive between 1 and 2 p.m.

Right on schedule, a giant C141 Starlifter aircraft of the U.S. Air Force flew into Damascus Airport soon after noon, ready to take the hostages to Frankfurt on their way home to the United States.

U.S. Ambassador William Eagleton, who had returned secretly Thursday to take charge of the final, detailed arrangements, left for the Lebanese-Syrian border, where he planned to welcome the hostages' motorcade.

He remained there four hours in vain, returning after a Syrian Foreign Ministry official arrived to inform him of the delays in Beirut.

Well after dark, when hope had been abandoned for the hostages' transfer before Sunday, both American and Syrian spokesmen were at a loss to explain what had gone wrong.

American officials said, "It is a great disappointment" and "We are totally mystified."

Some Syrians questioned the wisdom of President Reagan's remarks last night in which he condemned the hijackers as "thugs and murderers and barbarians."

They did not necessarily disagree with the value judgment, but they wondered if such language had not provided radical Shiite elements of the pro-Iranian Hezbollah with a pretext for refusing to hand over the remaining four hostages to the protection of Nabih Berri's more moderate Shiite Moslem militia, Amal.

A high-level Syrian source said, "We are still hopeful that the situation can be straightened out soon," but provided no further elucidation.

Earlier, both Kamal Assad Elias, the presidential foreign affairs adviser, and press spokesman Gebran Khourieh uncharacteristically had allowed themselves to be quoted by name in extolling the agreement and Syria's key role.

So buoyant was the mood that a Foreign Ministry official remarked, "Maybe now the Reagan administration won't denounce Syria as a center of terrorism."

Khourieh, in a statement assuming that the release of the hostages had taken place, said, "Syria hopes that every party concerned will fulfill its commitments and that the Lebanese prisoners in Atlit Israel will soon be released." Elias said, "We are happy with the results as reached."

And the official Syrian news agency SANA issued a statement noting that thanks to the "good offices" of President Hafez Assad, the "hostages were freed today and will be transferred to Damascus . . . .

"Syria, after the effort it made that led to the release of the hostages, hopes that all parties concerned will be committed to, and will honor, their undertakings in this connection."

That wording did not divulge what those undertakings entailed. But the statement made clear that they did not bind Israel directly.

It read, "Syria also expects that the Atlit prisoners will be freed." No time limit was mentioned.