West Brom's Shane Long and Manchester City's Edin Dzeko both scored after De Gea was slow to get down to low shots.
"Some of the media has been a bit judgmental based on the first couple of games," said Smalling.
"He has trained really well this week. You can see his agility and kicking. He will be a great goalkeeper for us."
United signed De Gea from Atletico Madrid in June, in a deal thought to be worth £18.9m, after his predecessor Edwin van der Sar retired at the end of last season.
Despite the 20-year-old's mistakes, United won the Community Shield with a 3-2 victory over local rivals Manchester City and opened their Premier League defence with a 2-1 win over West Brom.
Smalling also experienced the pressure associated with being a young and expensive United recruit when he arrived from Fulham for about £7m, and he backed De Gea to come good.
"He has always performed well for Atletico Madrid and our manager has put a lot of faith in him," Smalling told BBC Radio Manchester.
David de Gea conceded 11 goals to shots from outside the area in the Spanish League last season - more than any other goalkeeper
"It's only a matter of time before the whole world sees what a good goalkeeper he is."
Smalling admitted that the loss of captain and central defender Nemanja Vidic to a hamstring injury for up to five weeks requires the rest of the team's rearguard to raise their game.
"He has been such an influential player, especially last season," Smalling added.
"A lot of our stability was down to him, so it's going to be important that other players step up to the mark as he's going to be a big loss."
BBC Sport
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