Villa took the lead early in the first half through Gabriel Agbonlahor's effort, but were soon pegged back after Roland Lamah headed in his first Premier League goal.
Villa were able to hold on for a much-needed point against a Swansea onslaught, however, as they moved a little further away from the relegation battle beneath them.
Speaking to Sky Sports, Lambert said: "It's a game that I'd have loved to have won.
"It's a plus point, no two ways about it. It stops that sequence of losing games."
Asked whether taking the lead in the game was crucial, Lambert said: "It was, and the one thing I can't criticise the lads for is effort. They've got that in abundance.
"People talk about experience, but we've got a young side that are willing to do it, which is a big plus."
Despite being dominated in another game in front of their own fans, Lambert moved quickly to alleviate fears of another relegation battle at Villa Park.
"Virtually the spine of our team is a young, young side," Lambert said. "We're 18 months into this project as such.
"We're halfway there, and if you look at the table there's teams far more experienced than ourselves."
When asked again how he feels his Villa side performed against Swansea, Lambert was vocally supportive of his side.
"I'm not so sure how many saves Guzan's actually made and had to be called upon", he said.
"You can have all the possession you want, but you have to put the ball in the net. That's something neither team could do."
Villa came into the game without misfiring striker Christian Benteke who, despite his goal drought, still serves as Villa's main goal threat.
Captain Ron Vlaar was still missing for the Villans too, and Lambert pointed to the two absentees as reason not to panic for the fans ahead of a crunch clash against Sunderland on New Year's Day.
On Benteke's chances of making the Stadium of Light trip, Lambert said: "Hopefully he'll be back for that one, and we'll see how (Ron) Vlaar is.
"As I've said before, that's a big bit of your team: two lads that have been really good for us.
"From that point of view, if we get them back then great."