An own goal from Nathan Baker had given the Royals a valuable lead and looked set to plunge Lambert's side deeper into relegation trouble.
But Christian Benteke continued his excellent season by instantly levelling for the visitors before Gabriel Agbonlahor grabbed a vital goal just before half-time.
And the Scot insists his team don't look a side that are 'fighting for their lives'.
He told Sky Sports: "The lads were fantastic today. I thought we deserved to win and some of the play was absolutely brilliant. The second goal was fantastic.
"The confidence was always there and if you look at it today, it's not as if they're a team that look as though they're fighting for their lives.
"We've got a lot of confidence about us at the minute and a lot of enthusiasm for the game. They're young and they've got a great hunger to go and succeed.
"Every game is massive. If you look at the table now, there are a lot of teams that will be looking over their shoulder now."
Premier League To Stay Up 12/13 To Stay Up: Aston Villa 1/100
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