Villa earned a 1-0 win against Norwich City at Carrow Road in the Premier League on Saturday, as Czech striker Libor Kozak notched his first goal for the club to seal the points.
However, the victory came at a price for the visitors, with Kozak's introduction prompted by star attacker Christian Benteke limping off with an apparent hip problem.
And, although Lambert is confident that Benteke will make a quick recovery, the Scot admitted his squad are feeling the strain as they prepare to host Andre Villas-Boas' men on Tuesday.
"The good thing with Christian is he's usually a quick healer," he told The Express & Star . "I don't know how long (he will be out), we'll have to just wait and see.
"Westy (Ashley Westwood) hurt himself in training. He's just got a little strain. He’s been brilliant for us. To lose him was a blow.
"(Antonio) Luna just trained on Friday so he was touch and go, obviously (Jores) Okore's out, Gabby's (Gabriel Agbonlahor) hurt his ankle, Fabian (Delph) has been struggling so the lads were running on empty.
"We've played a lot of games in a short period of time."
Villa also host Manchester City on Saturday as they target their third Premier League win of the season, and Lambert is hopeful his team can get through a demanding week.
"We'll do our best to try to get through the Tottenham tie, but it's a massive game next Saturday," he added.
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