The England Under-21s international was a surprise departure on deadline day, joining the German club on loan until the end of the campaign.
Lookman had been used 13 times in all competitions this season and was expected to further feature in the remainder of the campaign, with Allardyce appearing to rule out a loan move earlier this week.
Asked to comment on the short-term deal, which does not include the option to make it permanent in the summer, Allardyce told Sky Sports News: "He was adamant he was choosing Germany.
"Going on your own at such a young age and not being able to speak the language is a massive challenge for his development. We tried to persuade him not to."