"All the teams in Europe will look and see the 5-2 win by Arsenal, away and with a young team, and I think they will be scared to play us," said the 19-year-old winger.
"That's the impression we want to give out to all the other teams. We do that and we have always got them on the back foot and hopefully we can just keep performing like that.
"It was absolutely brilliant. The main thing was getting the three points and everyone got their jobs right today. We scored five goals and it was nice to see us taking our chances.
"We knew their fans would be right behind them. But we quietened them down straight away by scoring two very early goals - it was a brilliant performance." But despite the one-sided scoreline, Walcott warned his team-mates there is still room for improvement, saying: "We will have to study this game ahead of the next one. We just need to take the positives out of last night because it's something we need to learn from.
"There were quite a few negatives as well but it's not going to always be perfect every game. Everybody wants to keep a clean sheet. But it was definitely perfect in the final third."