The Gunners moved back above north London rivals Tottenham with a 4-1 win over Wigan at the Emirates Stadium on Tuesday night, which confirmed the FA Cup winners' relegation.
Arsenal now head to Newcastle on Sunday with their destiny back in their own hands, a point ahead of Spurs following a superb nine-match unbeaten run since losing at White Hart Lane on March 3, and could yet finish above Chelsea should the Europa League finalists slip up against Everton.
Walcott, who took his tally to 21 for the season with a crucial second goal, has every confidence Arsene Wenger's men can now finish the job at St James' Park and deliver a 16th successive shot at Europe's elite club competition.
"We just have great experience in knowing what to do when the time is right. It is funny. It happens every year," said Walcott.
"We tend to finish very strong. I think it is just because the players want it so much.
"It (Champions League football) is big for the future of the club and the players. We have been in it for the last 15 years and we don't want to be the players who are not part of that.
"We just need to show that in the mid-season and at the start and we could hopefully be even higher than we are and not have this situation we are in.
"But it is very positive, and we will be fighting strong on Sunday."
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- Arsene Wenger