Walcott returns to the Emirates on Saturday evening two weeks after leaving, having already scored twice in victory over West Brom.
“I can't say what Arsene (Wenger) thinks but the opportunity to take a player with last season's goals record and that quality wasn't a big decision for me," said Allardyce.
“The bigger decision was (£25m for) Cenk Tosun because that is a much bigger risk (on a player new to English football) but we are short of goals.
“With Theo, a lot of things have been said - he hasn't reached his full potential and all that – but I don't know how you could say that after last season's performance: 30-odd games, 19 goals.
“He can be a key player for Everton now."