In the late Monday night vote, 274 members favoured the motion against 12, London-based Asian Lite newspaper reported.
Recognising Palestine as a state would be a "symbolically important" step towards peace, British MPs supporting the motion said during the debate. They highlighted Israel's disproportionate attack on Gaza last summer in which over 2,000 people were killed.
Morris said relations between Israelis and Palestinians are "stuck at an impasse".
The vote is symbolic but could have international implications.
In 2012, the UN General Assembly voted to upgrade the Palestinians' status to that of "non-member observer state". The assembly voted 138 to nine in favour. Britain abstained from the vote.
British Prime Minister David Cameron and his cabinet colleagues abstained from the vote on Morris's motion which states that "this House believes that the government should recognise the state of Palestine alongside the state of Israel".
Current British government policy, as set out by former foreign secretary William Hague, is that it "reserves the right to recognise a Palestinian state bilaterally at the moment of our choosing and when it can best help bring about peace".
Opening the debate, Morris told MPs recognising Palestine would be a "small but symbolically-important" step towards peace.
He said he would support an amendment from Labour's former foreign secretary Jack Straw to recognise Palestine as a state as a "contribution to securing a negotiated two-state solution".
"There are rejectionists in both Israel and Palestine, those that oppose any type of political settlement, and they would be delighted to learn that the British Parliament has refused what the vast majority of states around the world have already accepted," he said.
Former foreign secretary, the Conservative Sir Malcolm Rifkind, said he too wanted to see a two-state solution but added: "Symbolism sometimes has a purpose, it sometimes has a role, but I have to say you do not recognise a state which has not yet got the fundamental ingredients that a state requires if it's going to carry out its international functions and therefore, at the very least, I would respectfully suggest this motion is premature."
The vote comes amid moves elsewhere in Europe to recognise Palestinian statehood officially with more than 100 countries having done so.
Israel says moves to recognise Palestine are premature and undermine efforts to reach a peace settlement between the two sides.
Ahead of the debate, the prime minister's official spokesman said: "The government's position is very clear and hasn't changed, so I think that is a very clear indication of the British government's approach.
"The government's approach is a long-standing one and is in support of a two-state solution and we will continue to work with a range of international partners -- Israel, the Palestinian Authority -- in support of that."