Just a few weeks after Spurs beat Villa 4-0 in the Capital One Cup, Andre Villas-Boas' side collected the points in the Premier League thanks to goals from Andros Townsend and Roberto Soldado.
The defeat means Villa have now lost three of their four league games at home, but Lambert is confident his team are heading in the right direction.
"I've seen the progress since the start of the season and, if we play like that, we'll win more games than not," Lambert told Sky Sports.
"I didn't think there was too much in the game in the first half, it was pretty tight. I thought we started the second half well and looked as if we were going to get a goal.
"I thought we were playing well and looked pretty decent. I can't fault the lads for effort, that was great, and on another day we might have got something."
Christian Benteke returned to action as a second-half substitute after a month out with a hip injury and he came close to scoring for Villa.
The Belgian striker headed a good chance over a few minutes before Soldado scored Spurs' second and Lambert acknowledged it was a key moment in the match.
The Villa boss added: "I think in the big moments in big games, you've got to try and take them. But he's just back and he will score many goals for us, that's for sure.
"He has been out for about a month and has only trained a couple of days with Belgium and ourselves, so we'll see how he does over the next week."