Education Secretary Michael Gove shouted "disgrace, you're a disgrace" at Conservative and Liberal Democrat rebels following the historic House of Commons vote, an MP said.
The Scottish National Party's Westminster leader Angus Robertson told Sky News he watched on as Mr Gove had to be "persuaded to calm down" following the outburst.
He said "emotions were running high", adding: "This is an unprecedented defeat for the Conservative-Lib Dem coalition, for the Prime Minister David Cameron and for Nick Clegg, so obviously there were senior figures in the Government who were very upset that a number of their colleagues voted against the Government and abstained."
He continued: "I watched the English Education Secretary Michael Gove shout, 'A disgrace, you're a disgrace' at a number of Conservative and Lib Dem rebels. He had to be persuaded to calm down by a number of his colleagues. I retorted, 'It's called democracy', because that was what happened. We have finally learned the lessons from Iraq."
Labour peer Lord Reid of Cardowan, who was defence secretary under Tony Blair in 2005 and 2006, said it was the handling of the issue by the Prime Minister and Foreign Secretary William Hague which "has resulted in the shambles we have tonight".
Asked about Mr Cameron's position, former Lib Dem leader Sir Menzies Campbell said: "It's loyal to say things will go on as ever. The truth is they have been damaged. But the truth is some of the damage was done by very many of the same people that voted against them tonight earlier this year when it came to the question of the European Union."
Defence Secretary Philip Hammond told BBC's Newsnight programme that Mr Cameron was "disappointed" by the vote but was clear that "the mood of Parliament is that Britain should not be involved in military action and Britain will not be involved in military action".
He said: "We are now clear that we are not now going to be part of any military action - that probably means we will not be part of any planning or discussion. It is certainly going to put a strain on the special relationship.
"The Americans do understand the parliamentary process that we have to go through. They have always understood that in order to be involved in military action we would have to secure the consent of Parliament. I think perhaps they have been surprised by the scale of opposition in parliament - perhaps they will struggle a bit to understand the special reasons there are for that view."
General Lord Dannatt, former head of the British Army, described the vote as a "victory for common sense". He added: "President Obama may well take note of what's happened in Westminster tonight and think again - I certainly hopes he thinks again because I'm absolutely convinced the use of explosive ordinance into Damascus at the present moment will make the situation in that very difficult Syrian civil war worse, not better."