De Gea, signed from Atletico Madrid for ?20million in the summer, has made a nervous start to his career with the champions, with manager Sir Alex Ferguson taking him out of thefiring line for the mid-week Champions League draw at Benfica.
Man up: Pallister fears the physicality of the Premier League could hamper De Gea's progress
His replacement, Anders Lindegaard, impressed in his place in Lisbon - the Dane sending out a clear warning to his Spanish colleague that he intends to fight for the No 1 jersey.
United legend: Pallister was speaking on behalf of Barclays Ticket Office
But Pallister, who won four Premier League titles with United in the 1990s, has little doubt De Gea will establish himself.
The former England international claimed that legendary United stopper Peter Schmeichel suffered similar difficulties after arriving from Brondby in 1991.
Pallister said: 'There are similarities. Peter came over with a terrific reputation and found it difficult in his first few games in this league because it's a lot more physical.
'Where he was playing in Denmark or where De Gea was playing in the Spanish league, you're now going to get people standing on your toes at corners or barging you on the goal line to get the ball in the back of the net.
'It's something he will have to come to terms with but it's happened to the very best, so who's to say he won't deal with it? I think he will.
'He looks a very slight lad, he may have to bulk up a little bit. But I think there is belief in the club he will stand in good stead and I think he believes in himself. I think he will be a success.'
Let's get physical: Pallister (right) in his prime
Pallister feels the 20-year-old stopper needs to be given time to build his confidence and develop an understanding with the defenders in front of him.
He added: 'The centre-halves and the goalkeeper have to develop a relationship as well. You have to understand whether the goalkeeper is going to deal with balls coming into your box or whether he will let you deal with it. That will come with time as well.
'The defence can help by talking to him. Certainly the way he saved that penalty against Arsenal, the way they celebrated telling him they were right behind him, shows they trust him and want him to do well. And I think by giving something back to the Old Trafford crowd, that is very important for his settling-in period.'
In a flap: De Gea has looked vulnerable from corners
Pallister is also full of praise for Phil Jones, claiming the defender could go on to establish himself as an England regular.
The ?16.5million summer arrival from Blackburn has impressed at the start of his United career and Pallister thinks the 19-year-old has what it takes to rise to the top.
He said: 'It's easy to get carried away with his start at Manchester United. But you have to look at the maturity he's got and the type of character he is.
'He dictates to other people on the pitch, which is very rare for a young lad, and it shows he has a lot of confidence and belief in himself. He has been right out the top drawer.
Outstanding: Phil Jones (centre) has really impressed Pallister
'You never know the pitfalls ahead, but on talent alone he has a big England future.
'He has been absolutely outstanding. I didn't expect him to play too many games so early in his career there, but injuries to Rio [Ferdinand] and Nemanja [Vidic] have seen him come in and look an outstanding prospect.
'He plays with great maturity and doesn't appear to have any kind of weakness in his game.
'He looks a real big star of the future. For a player to come in at that age and be as settled as he is says a lot about the kid's temperament.'
Gary Pallister was speaking on behalf of Barclays Ticket Office. Every 90 minutes throughout the season Barclays is offering fans the chance to win free tickets to Barclays Premier League matches by going to a Barclays ATM and requesting a receipt, or by visiting www.barclaysticketoffice.com.
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