After suffering a 2-1 defeat to Chelsea at Stamford Bridge on Sunday, Arsene Wenger's men now sit sixth in the Premier League, seven points behind fourth-placed Tottenham and nine behind Rafa Benitez's side, which is in third.
The 23-year-old finally signed a new long-term deal with Arsenal last week after months of speculation and the England international claims the improvement of the squad persuaded him to commit to the club.
"I signed my new contract because I believe this team is getting better and we don't want to be standing still," Walcott told reporters.
"We've got to start clocking up points fast. We were out of the top four for quite a while last year as well and still managed to finish third, so we can't start worrying about what Spurs are doing."
Despite suggesting the personnel in Wenger's squad has improved, Walcott concedes the players lack confidence and has urged his teammates to start stronger in matches after goals from Juan Mata and Frank Lampard saw Arsenal trail after just 16 minutes in Sunday's defeat.
"I think there's a lack of belief here. We need to start realizing just how good we are. We've got some very, very good players but some of them don't believe they are good enough at times," Walcott said.
"We showed some great stuff in the second half at Chelsea and that didn't surprise me. But we can't be coming out of the blocks as slowly as we have done.
"As soon as we pressurized Chelsea after the break we showed what we can do. But we need to play like that for 90 minutes, not just the second half."