The Foreign Secretary will hold talks in London today with US Secretary of State John Kerry as Washington seeks to bolster international support for an armed response.
He insisted the US remained “very committed” to the so-called special relationship despite MPs defeating David Cameron to vote against a strike at Bashar Assad’s regime.
Mr Hague said he was determined to ensure Britain does not “matter less” in the world in future.
Speaking on BBC1’s Andrew Marr Show, he said he recognised there was “a lot of public unease about intervention overseas”.
“Be reassured that we have learned lessons of Iraq. We are not seeking to be drawn into wars in the Middle East. We now make decisions in a completely different way,” he said.
“We are not a government that is gung-ho about military action.”
But he said Britain must also not “turn in on ourselves”.
Mr Hague added: “Britain has great and positive influence in the world, and we must make sure that we retain that. I am very determined, as the Prime Minister is, that we will not matter less.”
The Government was “not planning to go back again” to the Commons for another vote, he said.
“If circumstances change dramatically, then of course everybody would be looking at things in a different light,” he accepted.
But he said there was “no guarantee” that Labour would not repeat its “rather opportunistic and partisan” decision to oppose the Government motion.
Mr Hague said it was right for the UK to supply the Syrian National Coalition with non-lethal equipment. “As in any country, there are millions of people who just want peace and democracy and freedom.
“We have to make sure that they are not eliminated, that they have a role, otherwise there won’t be a peace for Syria.
Ahead of his meeting with Mr Kerry, he said: “They were disappointed with our vote but we are a democracy and therefore we respect the outcome.
“They are very understanding about that.
“They are very committed to what we call the special relationship which goes much deeper and broader in our economies and our intelligence-sharing and so on.”