The former Bayern Munich midfielder (pictured, right) came on as an 80th-minute substitute in the 1999 Champions League Final when his team were leading 1-0 before United scored two stoppage-time goals to snatch the trophy from the German side's grasp.
He is not out for revenge on Tuesday and his charges would be the first to admit they are underdogs for the Group C game at Old Trafford.
"If you are not careful playing a team like Manchester United you end up paying," Fink told a news conference on Monday.
"It's not a question of getting equal... it was a great memory although it was defeat. I think you gain strength from defeat, they say that everything that hurts helps you improve."
Basel striker Alex Frei said the Swiss side were outsiders and that he was "hoping for a small miracle."
"We are not expecting to make the impossible possible but why can't we do something here tomorrow? Certainly we'll have the passion, 100 percent commitment and we'll see what happens when we come out of the 90 minutes on the pitch," he said.
That final comment set alarm bells ringing for Fink, who remembers how Bayern would have won that 1999 trophy if the whistle had blown on 90 minutes and not once Teddy Sheringham and Ole Gunnar Solskjaer had netted in added time.
"Of course in Manchester you have to say 92 minutes," he reminded Frei to a chorus of laughter around the room.
