The confident victory in his first game in charge made sure of Ajax's Europa League berth next year, even if Auxerre's defeat at Group G winners Real Madrid made the San Siro result irrelevant with the Dutch side finishing third in any case.
Demy de Zeeuw rifled home from the edge of the box after 57 minutes before Toby Alderweireld smashed in a beauty on 66 minutes as Ajax quickly forgot Martin Jol's surprise resignation as coach on Monday.
"We really demonstrated the courage to try things. We showed the philosophy of Ajax, building from the back. It's a positive thing, we were a real team," De Boer, caretaker until the Dutch league's winter break, told a news conference.
"Yes if it's possible I would like the permanent job, but it's not me that decides, it's results and the directors. I will put all my energy into to it and we'll see."
De Boer, a cultured midfielder with the Netherlands, Ajax and Barcelona, is also assistant manager to the Dutch national side and the experience picked up en route to July's World Cup final has rubbed off well.
"Football is simple. The players followed the instructions I gave them," he added.
SHAKY FORM
Milan were already certain of finishing second and going through to February's Champions League 16 and coach Massimiliano Allegri was not too down about his side's lacklustre performance given he rotated his squad.
"They had a lot more motivation," he said. "Definitely if we had had the obligation to get a result tonight we would have done. Tonight can be looked at apart. But I'm sorry, it's a Champions League game and we always want to do well."
The coach, whose side are riding high at the top of Serie A in contrast to their shaky form in Europe, rested top scorer Zlatan Ibrahimovic for the first hour and gave the out-of-favour Ronaldinho his first start in eight matches.
The Brazilian put in an average display which will reinforce rumours the former world player of the year could leave Milan in January now his powers are fading and he is no longer a fixture in the starting lineup.
The positive impact Ibrahimovic made when the Swede was introduced on the hour will also strengthen accusations that Milan are little more than a one-man team with fellow striker Alexandre Pato injured and Filippo Inzaghi out for the season.
"At the moment the most important thing is to get Pato back in early January," Allegri added.
"If there is the possibility to bring in another forward, I think the club is willing."
