Washington (CNN) Despite President Trump's deference to Russian President Vladimir Putin at their post-summit press conference in Helsinki on Monday, several senior administration officials say the State Department is not getting bombarded with concerns from US allies because they have concluded that Trump and Putin did not make any firm agreements.

"There isn't a lot of clean-up because there doesn't seem to be a lot of spillage," one senior official said. "The feedback we are getting from the Europeans is that they are relieved. They were worried he was going to give away the store and he didn't. So they aren't thrilled with the optics, but they are fine."

The immediate diplomatic reaction to Trump and Putin's press conference was scathing. European envoys offered assessments that ranged from "frightening" and "devastating" to "an abomination," with some raising the need to create new strategies to deal with the US as a now less-than-reliable ally, perhaps even an adversary.

Trump's endorsement of the Russian President over his own intelligence services and his failure to confront Putin on key issues such as Crimea and the Novichok poisonings in the UK signaled to many that he was giving Putin carte blanche to do what he wants.

But days after the summit it seems the level of alarm has subsided a little.

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