The England striker scored the fifth goal as the Gunners thumped the Royals and at the heart of the visitors' attack.
The 23-year-old's contract talks with the club are reportedly stalling over his desire to play centrally but he insisted he expects a resolution soon.
"Talks are ongoing and it's going to be a slow process,” he told Sky Sports. “Like I've said before in recent weeks this takes a long time, but I'm sure something will happen soon."
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“We're a big family, we know our qualities, we know it hasn't been good enough in recent weeks, but hopefully we showed people the true Arsenal,” he continued.
"They were some disappointing goals we conceded but going forward we looked very strong and now we've got a busy Christmas schedule."
Walcott’s team-mate Jack Wilshere was thoroughly impressed with the striker’s performance, and is hopeful his compatriot will be able to remain at the Emirates Stadium.
“That's between Theo and his representatives and the boss, but hopefully we can sign him up here,” Wilshere said.
"He showed tonight he can play up front and hopefully we can sign him up and he can play up front in the future."
The 20-year-old was also pleased to see Arsenal get back to form with a much-needed win after their disappointing Capital One Cup exit.
“It's been a tough week,” he added. “It was a disappointing result in the week and we knew we had to come here and be strong against a strong Reading team.
“I think we saw the old Arsenal tonight. We played some of our old stuff tonight and we need to continue that going forward."