But victory against West Ham moved Villa up to 17th place after bottom-six rivals Queens Park Rangers, Wigan, Reading and Newcastle all lost on Saturday.
"We deserve a lot of credit for what we have done today," added Lambert. "That was a huge win for us, especially with the results yesterday.
"We've taken a lot of knocks but football is a funny game and we are only three points behind Newcastle now.
Allardyce bemoans Hammers finishing
"We know what we have got to do and there's 12 games to go and every game is really tough. But you only enjoy these type of matches when you hear the final whistle.
"We have been a couple of goals up and not won twice recently so if we had taken those points then we would be comfortably in the middle of the table."
Lambert was forced into a late change with striker Gabriel Agbonlahor ruled out with a virus.
However, Lambert surprisingly gave a first Premier League start to 21-year-old Jordan Bowery, instead of £18m club record signing Darren Bent, although Bent came on to replace Bowery in the second half.
"There has been a virus going around the club and Gabby (Agbonlahor) had it last night and this morning," said Lambert.
"I didn't have to change the system, just the personnel and I thought Jordan (Bowery) did fine."
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