De Gea was signed from Atletico Madrid for £18.3m last summer as a replacement for van der Sar, who retired after six years at Old Trafford.
The Spaniard was criticised early on in his career at United but steadily improved and appears to have seen off the challenge of Anders Lindegaard to become the club's first-choice.
And van der Sar has rejected criticism that de Gea is too weak to command his penalty area and believes the 21-year-old will come into his own.
"I was also young and made my mistakes at Ajax, Juventus and Manchester United," said van der Sar.
"The main thing is about how you recover in the next game or perhaps that game itself (after making a mistake), and he recovered from it, became more important and made good saves.
"Presence-wise it was maybe hard to follow in my footsteps. But he has got to play his own game and be helped by (goalkeeping coach) Eric Steele and the manager, and next season hopefully he will be ready from the start.
"Is he too short to play in England? Well I haven't seen him in his shorts but I am sure that they found out when they went to sign him what to expect and how big and tall he would be."
And van der Sar believes United will have been rocked by losing their Premier League title to Manchester City in the final seconds of the season.
Sir Alex Ferguson's side appeared certain to retain their title until City scored twice in injury-time to beat QPR and snatch top spot - and van der Sar says that would have hurt, especially after being knocked out of the Champions League in the Group Stages and in the FA Cup Fourth Round.
He added: "There were two big disappointments early in the season, getting knocked out in the Champions League and FA Cup, and I don't think they anticipated not to be champions.
"In the last game when you have the last 25 to 30 minutes and QPR were winning at City you start believing.
"Of course the disappointment in the final two or three minutes would have been great. It was even for me sitting back in Holland and watching the games on two TV channels simultaneously.
"But they kept a lot of clean sheets even with Nemanja Vidic out injured, de Gea coming in and Lindegaard playing some games.
"They had a lot of injuries and changes in personnel, but to lose it in the last seconds - well City were on the receiving end a few years ago (when United won 4-3 in the final seconds in September 2009) so they got one back now, a big one."