The England winger believes that his strike in Tuesday's 4-1 victory over Wigan was one of his most crucial yet, but he remains focused on Sunday's game against Newcastle.
Arsene Wenger's side eventually cruised to a 4-1 victory over the FA Cup winner on Tuesday evening after scoring three goals in eight second-half minutes.
"Wigan coming off an absolutely fantastic FA Cup win, we always knew it was going to be difficult – every game is very difficult this season in the Premier League – and they showed great quality," he told Sky Sports. "It was probably a fair result at half time, to be honest, going in at 1-1. I felt they did play the ball quite well, but we've got to show character and we did. We came at them in the second half and showed them what we're really made of."
Walcott's strike put the Gunners ahead for the second time on the night, and was his 14th league goal of the season, his best tally in an eight-year club career.
"This is one of my most important goals and hopefully it can be a few more next weekend. Anything but the winner today. The guys did it, I'm so proud of them because we deserve it," Walcott said.
"I felt like we had to take the initiative really. We had to make runs in behind, we weren't really doing it in the first half, the final ball wasn't the best at times and we weren't really putting people in the box, and second half we did that as the first half showed."
A win for the Gunners at Newcastle on Sunday would guarantee Champions League soccer for the 16th year in a row for Wenger's side. Meanwhile, Wigan will play in the Championship next season after an eight-year Premier League stay.