City got back to winning ways after three games without a victory - the nadir being a 4-1 mauling at the hands of the Merseysiders - as they saw off Southampton 3-1 on Saturday.
The result took City back to the top of the Barclays Premier League and the title favourites now want to make sure they stay there.
Caballero, who took over in goal from injured England number one Joe Hart, said: "It was like a call with big attention - Liverpool played really well
They are a big team and we must be ready for every game and every team.
"I think we learned after this defeat and we started again
From the first minute, we were hungry to win.
"We needed to take the top of the table again as soon as possible
We needed to win
We can't concede another result at home again because we lost two games this season
I hope we stay in the first place of the table."
City started with a determination to put an end to their recent poor sequence, scoring twice in the opening 20 minutes through Kevin De Bruyne and, on his full debut, Fabian Delph.
Southampton rallied and replied early in the second half with a Shane Long header but the visitors were unable to capitalise further on a spell of dominance and were killed off by Aleksandar Kolarov in the 69th minute.
The downside for City was the loss of Sergio Aguero in the second half through injury but manager Manuel Pellegrini later played down the issue, describing it as a mere "kick in the heel" that he did not think was serious.
Caballero performed strongly, with good saves from Dusan Tadic and Long as Saints pressed in the second period
There were some nervier moments earlier on but it was generally a good response by the Argentinian to his critics after a poor display in September's 4-1 loss at Tottenham.
The 34-year-old said: "I think this was my best performance with this shirt but I will try to make a new 'best performance' in the next game
But I think we played really well and this is the most important (thing)."
Southampton's defeat was their first away from home in the Premier League this season but, aside from the difficult opening, their display was a positive one.
Long told the club's website: "After 20 minutes they were 2-0 up and it would have been very easy to roll over and let them get three or four.
"But we were confident in ourselves to get the ball and pass it around
I thought we did that and when we came out in the second half and got the goal, I thought we were right back in the game.
"We had one or two chances to make it 2-2 and that would have been it, but they are a hell of a side.
"Kolarov's goal to make it 3-1 killed us off but we can take a lot of positives
It's not nice to lose a game but when you lose it playing well it is a little bit easier to take."
Source : PA
Source: PA