Gabriel Agbonlahor broke the deadlock amid some poor Swansea defending in the seventh minute on Saturday, before Roland Lamah headed the visitors level nine minutes before the break.
And, while believing his side could have taken maximum points from the fixture, Lambert is glad Villa avoided losing five Premier League games in a row for the first time since 2001 following defeats to Fulham, Manchester United, Stoke City and Crystal Palace.
"It's a game where you'd love to win, there's no two ways about it," he said. "But a point stops that sequence of losing, which is vital for us.
"We're pleased to stop that sequence, it's a big point.
"We were without big players in that and it's a lot for us to carry - we're a young squad.
"Swansea are a good side, they pass the ball really well, but (Brad) Guzan's not had many saves I don't think, not many saves at all.
"They came here and played some nice football, but I'm delighted with the lads and their effort, because Guzan never really had that much to do."
Agbonlahor's opener sparked exuberant celebrations from the home side, who had netted just once in their last four outings, and Lambert believes this demonstrated the close-knit nature of the Villa dressing room.
"They're a group that are really close together and there's a good unity there that you need," he added.
