De Gea is already being compared with the Italian shot-dropper, who lasted just four games at Old Trafford after a £4.5million switch from Venezia in 1999.
Manchester United's new No 1 cost considerably more at £17.8m but has already been guilty of clangers in the Community Shield and at West Brom.
Boss Alex Ferguson says De Gea needs time. But it was in Taibi's fourth game, a 5-0 hammering by Chelsea, that the Scot finally lost his rag.
Speaking exclusively to SunSport, Taibi said: "Ferguson taught me a lot - even if he did have a right go at me after the Chelsea match.
"He is like a general. He is good in command but when he loses it, he loses it - and he really let rip at me in the dressing room after the Chelsea game.
"After that Ferguson, who I have the greatest respect for and is a top manager, decided not to play me any more."
Taibi, who conceded 11 goals in his four games, is now hoping De Gea is given considerably more time than he was. But he has warned the 20-year-old Spaniard he is facing intense pressure.
Taibi, 41, said: "Take it from me, being United's goalkeeper is not easy but David can still do it. He is only 20 and has the potential to be world-class.
"United want everything and want it straight away. I was only there for a few months as I made some mistakes and left, but David needs time.
"What I'd say to him is think about United's great keeper, Peter Schmeichel. He didn't have a good start there either and look what happened to him. He was incredible.
"David is young, he did well at Atletico Madrid and I'm sure he will do well at Old Trafford. He's one of the best in Europe, no doubt.
"He should keep cool and people should lay off him.
"He will have a chance to show his value and has the potential to be a great asset to United for the next 15 years.
"He should stay calm and not worry about anything. He's strong and in form. United is a great club with a great atmosphere, history and organisation."
De Gea's mistakes against Edin Dzeko and Shane Long are nothing on Taibi's most famous howler against Southampton.
He bent down to scoop up a mishit grasscutter from Matthew Le Tissier only for the ball to go through his grasp, between his legs and in.
But it was the first against Chelsea that sticks in his mind. Straight from kick-off, Dan Petrescu sent a cross into the United area and Taibi collided with team-mate Denis Irwin - enabling Gus Poyet to head into an open net.
Taibi added: "The 5-0 defeat against Chelsea sticks in my mind because I messed up with Poyet's goal. I felt really impotent in that game.
"After that, it all went downhill. It was my last first-team game."
Taibi, who always wore black tracksuit bottoms, says while the United fans were kind, the opposition faithful were not so.
He said: "I don't remember the United supporters giving me a bad time at all.
"The opposition fans were different and would always be making fun of me - especially after the ball went through my legs against Southampton.
"But I keep all four games I played close to my heart and still have a DVD of the game against Liverpool, where I won Man of the Match.
"My poor form was related to the fact I was having problems with my wife, even though our children and she loved Manchester. I'd have loved to have stayed but had to leave to save my marriage. Thankfully, it was sorted and we're still together."
Taibi played for 12 clubs before retiring in 2009 and is now general manager at Montebelluno, near Treviso.
Bizarrely, he is remembered in Italy not for his goalkeeping, but goalscoring.
On April 1, 2001, Taibi netted with a header for Reggina against Udinese to make it 1-1. He and Cremonese's Michelangelo Rampulla are the only keepers to score from open play in Serie A history.