Walcott took a knock to his knee and was was stretchered off towards the end of Arsenal's 2-0 win against Spurs at the Emirates Stadium on Saturday in the third round of the FA Cup.
The England international gestured the scoreline to Tottenham fans as he was carried away with coins thrown in his direction.
"Walcott was getting a lot of treatment, I think he had a knee injury and the coins started to rain down from the Spurs fans," said Jonathan Northcroft of The Sunday Times.
"He reacted and held up the 2-0 gesture and there were more coins as a result. Wenger said afterwards that it was a harmless gesture and he was smiling when he did it and no one should take offence to that.
"I don't think we should get too offended by this. A week ago Anelka made a truly repulsive gesture and that is something that everyone should look at. Jack Wilshere not too long ago made a rude gesture to supporters, this is a lot milder compared to that."
The Sunday Mirror's Andy Dunn believes that Tottenham will get into trouble for the missile throwing and believes Walcott should be publicly warned for his involvement.
"I suspect that Spurs will be in trouble and Walcott will basically be giving a warning - either formal or informal," said Dunn.
"I think the FA will say to him that he was a bit silly but Spurs will be in trouble because you cannot excuse the missile throwing that took place. I have to say that at best Walcott's gesture was a little bit silly but at worst it was provocative and there is no getting away from that. I think that referees should use a little bit of common sense too - the rule is to take the stretcher around the side of the pitch so Walcott had to go along a whole line of Spurs fans.
"Why don't they just tell them to go off the pitch the other way and avoid that? It would only be 30 seconds more. Instead he had to run the full gamut of the Spurs fans and something was bound to happen.
"My other point regarding the gesture is that clearly it is not an abusive gesture like Jack Wilshere made to the Manchester City fans but it is provocative and what the FA have to be careful of is setting precedence.
"If it is okay now for a player to go to opposition fans and signal the score then there is nothing stopping anyone else doing it. I don't think Walcott should be banned but he needs a warning and if it happens again then players could face a ban.
"Oliver Holt was on the show a few weeks ago discussing Wilshere. His point of view was if fans give it then they should be able to take it. I agree with that theory and I think most fans would agree that if they give players stick then they can give it back. But where do you draw the line? I think players need to be a little bit bigger than that."