The game ended 1-1 with City down to 10 men and their keeper Joe Hart pulling off some incredible saves to prevent a Liverpool win.
"I think we tried to play the same way we did last week against Chelsea," admitted Lucas.
"We knew they would have a lot of possession and the counter attack is always dangerous, so we tried to pressure and keep the ball when we could and try to create chances.
"I think we deserved the win but a draw is not a bad result."