Walcott scored two goals in Arsenal’s 7-0 win over Slavia Prague at the Emirates on Tuesday.
He said: “It was brilliant to train with Thierry for a year-and-a-half and take bits out of his game but I want to be my own player.
“I suppose people are always going to compare us because of the way I run and the fact that I can play out wide or through the middle.
“Straight after Tuesday’s game I heard that my second goal was a Thierry-style finish, which was nice to hear. But it was my goal.
“Everyone was disappointed when Thierry left for Barcelona in the summer but in a way people have forgotten about that now because Arsenal are doing so well this season. I’ve not spoken to him since he left but he’s doing brilliantly for Barcelona and we all wish him the best.”