Following their Carling Cup final loss to Birmingham City and elimination from the Champions League last year, the Gunners slipped down the Premier League table and finished behind Manchester City in fourth.
With Liverpool and Manchester United among their first three opponents next season, Walcott has admitted that the Gunners must make a fast start.
"We don't have any time to bed in at all," he told reporters. "We don't expect any game to be easy, but we'll be ready.
"We want to start off well and we want to challenge for something this year. Only time will tell what we do."
The 22-year old added that while the players share the fans' disappointment, they are looking repay their loyalty next season.
"Without a doubt, we owe the fans a good start. They have been so loyal to us when we have not been winning trophies, which we should be for such a big club.
"As players we are disappointed in ourselves, but that is in the past now. This year is a massive one for everyone, for the club itself.
"The fans are very important to us all and hopefully we can make them proud."
Walcott joined Arsenal from Southampton in 2006 and has made 114 appearances for the club.