Arsene Wenger’s side were 2-0 down at half-time in the FA Cup fourth round tie, only to rally after the break and score three goals in seven minutes.
It has been a testing time for Arsenal in January, with three consecutive Premier League losses in a row causing serious dissent in the Arsenal faithful – something Walcott feels was down to the players.
“That was for the fans. They have waited a long time for a great result and we gave them that on Sunday,” he is quoted on the official Arsenal website.
“Obviously the fans are entitled to their opinion and we wanted to do it for them in the second half because we weren't good enough [in the first].
A cantankerous mood around Emirates Stadium was transformed through the second half rally and it would have been a mighty relief to Wenger and his players to hear the crowd getting behind them again.
Villa scored mid way through he first half when sloppy defending at a corner led to Richard Dunne heading in Robbie Keane’s floated cross.
More slack defending on a Villains counter-attack led to Darren Bent finding space in the area and, after his initial effort was parried by Lukasz Fabianski, he slotted home a terrific finish from a very tight angle.
There were shell-shocked looks on the faces of the Arsenal team, as this was a game they had been dominating, but now feared the worst.
Walcott conceded that it was a close call but insisted Arsenal were the better team and should just be happy they are now in the next round.
“When you are at home you do not want to go 2-0 down, even if it was against the run of play. Villa took their goals well,” he added.
“On the set piece maybe we could have done better, but we are into the hat and we are looking forward to Sunderland or Middlesbrough.”