De Gea, signed from Atletico Madrid this summer following the retirement of Edwin van der Sar at the end of last season, conceded a soft goal but finished on the winning side at The Hawthorns.
The failure to make what looked like a routine save from Shane Long followed a difficult day against Manchester City in the Community Shield earlier this month, when again United recovered to win.
But Phelan and Smalling are adamant there is no cause for alarm.
"Young or old, goalkeepers make mistakes," said Phelan.
"We have got trust in him. He will be a good Premier League goalkeeper."
Smalling added: "He is making some good saves.
"His agility and kicking are excellent, we have seen that in pre-season. He is going to be a top goalkeeper."
Smalling, meanwhile, is sure United can cope in the coming weeks despite losing Nemanja Vidic and Rio Ferdinand for two and six weeks respectively.
In Ferdinand's case, his hamstring injury rules him out of United's first Champions League group game, plus England's Euro 2012 double-header with Bulgaria and Wales.
Vidic meanwhile, will miss home encounters with Tottenham and Arsenal as he nurses a calf injury.
Yet Smalling and Jonny Evans have already proved themselves to be able deputies when required and United also have the highly-rated Phil Jones in their ranks following his summer arrival from Blackburn.
"You don't want to lose your big players," said Smalling.
"Rio and Vida are leaders. For years they have been the main part of this team and one of the reasons why we have won so much.
"But with the (England) Under-21s over the summer, we all said we were hoping to get a chance.
"For it to actually happen is a different thing entirely. But the manager has shown that faith in us."
In addition to Smalling and Jones, Tom Cleverley and Danny Welbeck were also at the European Under-21 Championships in Denmark in the summer and started on Sunday, keeping more senior figures on the bench.
It did take the introduction of Dimitar Berbatov to help turn the match in United's favour though, Ashley Young's deflected effort ensuring the champions did not follow Liverpool, Arsenal and Chelsea in tripping over the first hurdle.
"It is brilliant," said Smalling.
"You never quite know what you are going to get on the first day of the season.
"It was all about getting the three points. The manager stressed at half-time that we had to make sure we were not one of the casualties.
"We were knocking on the door all through the second half and Ashley Young came up with something at the end.
"He has been great in pre-season and is just carrying on that form."