Lambert told reporters after the match: "It was a really tight game, a physical game, there was nothing much in the game, they took their chance.
"The game could have gone either way. It's a really fine margin in that game today. It is where it is, there's loads of teams and games still to play and you have to get over that finishing line as quick as you can.
"We saw a lot of ball and a lot of possession. There weren't too many chances for both teams."
Aston Villa, now in 14th place and just four points above the relegation zone, will welcome Southampton to Villa Park next Saturday.