A 3-2 reverse at home against Palace was followed by a 2-1 defeat at the King Power Stadium , though the reigning Premier League champions returned to winning ways with a 3-1 result at Southampton on Sunday .
The three points picked up on the road lift Pep Guardiola's men back up to second place in the Premier League table prior to their pivotal clash with leaders Liverpool on Thursday.
Goals from David Silva and Sergio Aguero, either side of a James Ward-Prowse own goal, made sure City took full advantage of Tottenham's defeat to Wolves a day earlier, with Kompany delighted with the performance following recent setbacks in their title defence.
"It was more than just the result - it was about the way we played," the defender told Sky Sports.
"We're not focusing on anything much other than our performance. We have to be hungry and aggressive.
"We've been hit in our pride recently and that's how a team has to react."
City and Liverpool fought out a goalless draw at Anfield in October but Kompany insisted his team would hold nothing back against Jurgen Klopp's Reds, who thrashed Arsenal 5-1 on Saturday.
"We want to kick on," said the Belgium international.
"We've got four competitions to play for in an incredible season. Today was a step in the right direction.
"We go into the next game in the same frame of mind, as always. We just want to win.
"We need to be ready for a fight and ready to take it to them [Liverpool] and try to win. We should be able to pull everything out of the locker for that game."