Oscar, Diego Costa and Willian found the net as Villa fell to their second consecutive 3-0 loss in the English top flight, following last weekend's home defeat to Arsenal.
But, despite bemoaning his side's inability to finish off their chances, Lambert felt his players could leave Stamford Bridge with their heads held high.
"When you come to places like this you've got to score, because in my own opinion they'll be close to winning the title, and I think they'll be close to winning the Champions League," Lambert said.
"It's hard to come here at the best of times, but I couldn't fault my own team. We gave it a right good go.
"We're playing without a recognised striker at the moment. I thought Gabby [Agbonlahor] did excellent the whole afternoon and I thought the three lads in the middle of the pitch [Fabian Delph, Tom Cleverly and Ashley Westwood] were excellent.
"When you come to places like this, if you get beat you've got to leave with your confidence intact, which we certainly are."
Lambert conceded that he did not expect to come away with much from his side's current sequence of fixtures, which had seen them win 1-0 at Liverpool and fall to that defeat against Arsenal prior to Saturday's clash.
"We're in a run of games which is really tough, but performance-wise - other than trying to get a goal - I couldn't ask for any more," he added.
"We're playing against top-class sides in Arsenal and Chelsea.
"If somebody said to me 'You'll take three points from Liverpool, Arsenal and Chelsea', I would certainly have taken it. We've taken three from Liverpool.
"So we're into a run of games where we know it's really tough. We're up against Manchester City next week, which will be really tough, and those four teams I've just mentioned will be there or thereabouts when the title gets handed out."
