John Spellar was the only Labour MP to vote against against a plan to update the school curriculum to include teaching about LGBT families.
The move was overwhelmingly backed in the House of Commons, with just 21 MPs voting against it.
Mr Spellar, MP for Warley, was heavily criticised over his decision, with the Liberal Democrats labelling him a "dinosaur".
He said he chose to vote against the move because of concerns from some of his constituents but after seeing more details about the plan admitted he should have voted in favour.
The changes, which have been led by Education Secretary Damien Hinds, are the first time in 20 years the curriculum has been updated and mean children will be taught about different family models from primary school, including same-sex couples and parents as well as lesbian, gay, bisexual and transgender identities.
A total of 538 MPs backed the move, which comes after a high-profile row about the teaching of LGBT rights at Parkfield Community School in Birmingham.
Mr Spellar told the Express & Star: "I think it was a mistake to vote against it. It was a mistake for which I apologise to the LBGT community There were a lot of concerns from faith communities.
"The education minister Nick Gibb put out an explanatory letter which indicated the way they are looking at local circumstances and wanting to engage with parents and that covered it."
He added: "We need to make sure faith communities are reassured. There was a lot of representation, it wasn't people who were demonstrating, just constituents and parents who had concerns.
"There does need to be engagement. People need to be persuaded and we need to make sure we are living in a tolerant and inclusive society."
Julian Donald, chair of the Wolverhampton Liberal Democrats, said: "I am appalled that John Spellar voted to turn back the clock on LGBT rights and not support inclusive relationship and sex education. Many people would say that was the action of a dinosaur. His vote is utterly shameful."
The co-chair of LGBT Labour, Melantha Chittenden, also criticised Mr Spellar.
She said on Twitter: "Woke up to find out that one Labour MP voted against LGBT inclusive relationship and sex education and I’ve been sat here trying to work out how to explain how furious I am, but I only have one thing to say: John Spellar shame on you."