Allardyce claimed earlier this week that the former Charlton Athletic forward would be going nowhere, having already let Kevin Mirallas and Aaron Lennon leave on temporary and permanent deals respectively this window.
Lookman was keen to play regularly elsewhere, however, and turned down the option to join a Championship side - thought to be Derby County - in favour of Bundesliga outfit Leipzig.
Asked if he was reluctant to sanction the deal, Allardyce told reporters at Friday's press conference: "I was, but he insisted so rather than have a player that was going to have the wrong attitude around the place. He wanted to play some football.
"I wasn't very keen on it based on the fact that we'd already let Mirallas go and Aaron Lennon, but he really wanted to get some football. We had the offer from Leipzig and we had another from a top Championship club.
"He chose Leipzig so he's got all of his choices to go and get some experience and hopefully a lot of first-team football in the Bundesliga, which for me is a very very difficult challenge for anybody for somebody at such a young age.
"From a football point of view, he's got a lot of talent but from a cultural and language point a view, he could find that difficult."
Lookman, in line to make his Leipzig debut against Borussia Monchengladbach this weekend, featured 13 times for Everton in all competitions before leaving.