"We upped it," Lampard told television reporters.
"In the first half we weren't at our best, a bit slow with the tempo of the game and we gave away a silly goal that allowed them to score.
"Once we upped it with a bit of pace in our game you could see a big difference.
"We had a word with ourselves at half-time."
Chelsea flew back into London from the Club World Cup on Monday, but the journey from Japan did not appear to take any toll in the second half, especially once Mata equalised just a minute after the restart.
Lampard said: "We didn't make the greatest preparation but there's no excuse, we had to up it.
"The early goal gave us the impetus, we believed from then on and we didn't think we could lose the game.
"Some of the football we played, we opened them up and showed what we could do."