The Gunners have endured a frustrating season as they fight with London rivals Tottenham Hotspur and Chelsea for a Champions League place.
Walcott believes that Arsene Wenger's side have the potential to challenge for the Premier League title next season if they can find form every week.
He told the club's official website: "If we get a bad result, you see a reaction. We shouldn't have to get a bad result and then perform well in the next game. It should always be there.
"The guys have got it. Mentally, they are very strong. It's realising how we cope when we come back from those disappointing results. We just need to do it every week, it's as simple as that.
"There's great potential there. We've had too much experience now to be challenging for fourth. We need to be challenging for the Premier League because that's what we want to be known for. We want to be in the history books, we need to win something now."
The Gunners currently sit fifth in the table after winning their last two league matches.