The England international was Arsenal's top scorer during the 2012/13 campaign, contributing 21 goals.
"I was very proud of being top scorer, but it sort of went unnoticed really," Walcott told Arsenal.com. "The season was hard work, everyone knows about the contract situation and to play with that on your mind is tough, but is was a massive achievement for me to be top scorer for the season for Arsenal.
"The likes of Thierry Henry, Robin van Persie and Dennis Bergkamp have done it, and now I want to push on from that. I don't want to stay at a steady level, I want to push on and push the Club on so we realise our potential.
"I was very proud of myself last season - not just the goals but the assists and what I contributed to the team itself. That has come from me believing in myself a bit more."