Arsene Wenger's side are currently fifth in the Premier League, two points off the fourth spot that is currently occupied by Chelsea.
The Gunners were knocked out of Europe's premier club competition after losing out on away goals to Bayern Munich on Wednesday, and Walcott has said that a club as big as Arsenal need Champions League football.
"It would be a tragedy for this team not to be in the Champions League," Walcott told The Mirror.
"We want to be at places like Bayern Munich again. The way we played in Germany shows how much we have underperformed at times this season.
"It's been up and down. For the big occasions, we tend to turn up – it's just very frustrating. We need to take the desire and confidence we showed in Germany into the Premier League."
Walcott signed a new deal with the club in January.