Sheringham scored the crucial equaliser in that final 20 years ago before current United boss Ole Gunnar Solskjaer netted a winner at the Nou Camp.
The Red Devils head back to Barcelona tonight, 1-0 down going into the second leg of their Champions League quarter-final.
Luis Suarez headed home Lionel Messi’s cross, via a Luke Shaw deflection, to give Barca the win at Old Trafford.
Messi was relatively quiet last week, especially after United defender Chris Smalling left him battered and bruised with a full-blooded aerial challenge.
And Sheringham doesn’t expect the Argentinian to have another off-night, while the former striker also recognises the difference between facing Bayern at the Nou Camp and facing Barca.
“It’s a bit tougher, overturning a Barcelona team who are 1-0 in front with Lionel Messi,” Sheringham told The Times.
“It doesn’t make things easy, it’s a really tough job they’ve got on their hands, while for us the Nou Camp was a neutral ground — daunting for us but also for Bayern.
“When you’re playing against Barcelona there, it’s a fortress and has been for years.
“When about to face Paris Saint-Germain [in the round of 16 last month] after losing the first leg 2-0, Solskjaer talked up how that tie wasn’t over and they could still go to Paris and win, and he’ll be saying the same this week.
“Whether he actually believes it, I don’t know.”
Manchester United go into the clash with Barcelona with plenty of news ahead of the match:
Plenty of fans are wanting United to use the spirit of 1999 tonight.
But Solskjaer is looking at a much more recent clash.
Asked whether he will speak to his players about 1999, the Norwegian said: “No I won’t because it was against Bayern Munich, it was a final, it was different.
“We will use the PSG (match), we will use Juventus away, we have beaten some good teams away from home this year, and played against some great players.
“We had (Barcelona) flustered at times here [in first leg] as well.
“Yes, they controlled the game towards the end, they had the possession but they never really bothered us in our own half.”