Walcott's 'effort' was denied by the match officials, though he did win a legitimate penalty for Arsenal's late equaliser.
Walcott issued a statement apologising for his actions.
The 21-year-old said on the club's official website: "I want to apologise to the managers because I actually dived. I was trying to win the penalty.
"I said to one of their players 'would you have done it?' and he said he probably would have.
"I am not the sort of player to do it, but I own up to it and apologise. It is something I don't want to see in my game."
Walcott continued: "I have heard some players say 'if there is a slight touch, go down' and it can work both ways.
"It was one of those things. I am not happy with myself for doing that, but I am happy that we got the draw.
"I had a little joke with the referee afterwards saying 'that was my first dive, can you tell?'
"I don't have to own up to it and I can't speak for other players, but I have just expressed how I feel. I hope people respect that."