The Birmingham outfit had a chance to move clear of the relegation zone after a run of four successive Premier League losses.
After the events of this week, that performance shows evidence of the players’ commitment
The Saints had the best of the opportunities at Villa Park, with American Brad Guzan doing well to deny midfielder Steve Davis.
Villa, who suspended assistant boss Ian Culverhouse and head of football operations Gary Karsa earlier this week, failed to test Southampton goalkeeper Artur Boruc.
Despite the stalemate which leaves Villa five points clear of the drop zone, Lambert praised his side’s performance against high-flying Southampton.
“To play the way we did in the second half, against a good Southampton side, I cannot fault the effort,” Lambert told BBC Sport.
“The lads deserve enormous credit and with their energy and desire I couldn’t be prouder. Our goal difference is pretty good, so we’ll probably need one more win [to be safe from relegation].
“After the events of this week, that performance shows evidence of the players’ commitment.”
Meanwhile, Southampton manager Mauricio Pochettino felt his side deserved three points.
“I thought we did enough to win the game but we are lacking luck and clinical edge in front of goal.
“We started off well, had 70% possession but are not taking chances. We are creating them and look like a team fighting to win the Premier League so I am happy with the effort.
“I saw the handball and I thought it was quite clear, replays also show it was clear but the linesman was close and he didn’t even see it.”
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