Weimann held his head in his hands after shooting wide from six yards with the goal at his mercy after Hammers goalkeeper Jussi Jaaskelainen had spilled Christian Benteke's low shot.
It looked like proving a costly error in Villa's fight for Barclays Premier League survival until second-half goals from Benteke and Charles N'Zogbia secured a 2-1 win.
But Lambert's faith in Weimann, Villa's second top scorer with nine goals, is unwavering after his side climbed out of the bottom three for the third time this season.
Lambert said: "I thought we should have had a goal in the first minute when Andi missed a chance and everyone was a bit hurt by that.
"It probably took Andi by surprise himself that he's missed it. He is one of the most natural finishers at the football club
"Heads could have gone down after the early miss but Andi Weimann has been brilliant for us this season.
"He has pulled us out of a few holes a few times and he will come back stronger than ever from that. He's only a young lad, people forget that. It's important he bounces back from it.
"One thing Andi doesn't lack is confidence, that's for sure. His effort and enthusiasm will stand him in good stead throughout his career."