The 23-year-old gave the Gunners the lead inside 60 seconds at Goodison Park with a well-taken finish before Arsène Wenger’s men were pegged back by Marouane Fellaini’s equaliser.
And Walcott, who has made no secret of his desire to be deployed as a striker, believes he is now much more confident when presented with goal-scoring opportunities.
“Those are the sort of positions [at Everton] that this season and in the last few seasons I have been quite deadly in,” said Walcott, whose future remains a subject of constant speculation, with the forward in the final year of his current Arsenal deal.
“When given a little sniff I am able to take it now. The goals [I have scored] show that.
“I think I scored 11 last season and 13 the year before. Not just that, but my general play [is getting better] as well. The assists are coming now, which is fantastic, and I am enjoying my football.
“I am very happy with the way I have started and it has got to continue. Hopefully I will take it into Saturday’s game [against Swansea].”