A late own-goal from Steven Reid which was created by Ashley Young gave the Red Devils victory, which spared De Gea's blushes after the United keeper had earlier inexplicably dived over Shane Long's shot to gift the Baggies an equaliser to Wayne Rooney's 12th-minute strike.
Ferguson believes the Spaniard will soon get to grips with the Premier League.
"The first 25 minutes we were superb, the movement of the ball was great, but then we slowed and lost momentum," he said.
"We lost a goal which David should have done better with.
"It was just a bit of concentration there but welcome to English football. He came in for it in the second half and I thought he should have been protected more by the referee, but it was a good experience for him.
"It's all a learning process."
United new boy Ashley Young admitted it had been a hard day's work at The Hawthorns.
The winger was instrumental in the decisive goal 10 minutes from time, when Reid turned Young's cross past Albion goalkeeper Ben Foster into his own net.
And Young was relieved his side prevailed in the end.
"It's the first game of season, we knew it was going to be tough coming to The Hawthorns but we have a never-say-die attitude and work to the final whistle, and we got our rewards in the end," he told Sky Sports 1.
"I thought we looked like scoring whenever we went forward, but we knew we'd have to grind it out and that's what we did.
On De Gea's earlier error, Young added: "Obviously he was disappointed with the goal, but we're always going to create chances throughout the 90 minutes.
"We're drilled to play to the final whistle and that's what we did."
West Brom boss Roy Hodgson thought his team's gutsy display warranted a point against the defending champions.
"It was close," he said. "Our performance was very good, and we're sad not to hold on but very pleased with our team's performance.
"We played ourselves into the game and deserved a result for long periods of the game, but unfortunately Young got that bit of luck and that changed the complexion of things.
"We knew it was going to be tough, but we kept our end up well and consider ourselves a little bit unlucky not to get something from the game.
"We gave United a good run for their money."
Hodgson was, however, delighted with Long's goalscoring performance on his debut.
"It was a good start for Shane Long," he added. "His performance in general was very good, we did enough to get ourselves a goal and it's always nice to score on your debut.
"I'm delighted for him, and his work rate and his general performance was deserving."