Nicolas Anelka equalised and Malouda - who had been left out of the side but came off the bench in the first half - ensured the Portuguese's first three points in charge.
Villas-Boas said: "In the first half, we suffered a little bit from anxiety because we suffered the first goal too early and we couldn't express ourselves.
"I think it has nothing to do with the impact of the changes we made.
"Our half-time talk was for the players to free themselves from the anxiety they were suffering, because the public was anxious and the players were anxious and you still have 45 minutes to play and anything can happen - and it did happen.
"When you find the back of the net for the 1-1, again the emotional impact on the opponent is tremendous and we felt very, very confident to go in search for the second goal, and we found it."