The Blues were reduced to ten just after the half-hour mark, when Fernandinho was sent off for a challenge on Johann Berg Gudmundsson.
Guardiola’s men rallied after the break, earning a two-goal lead through goals from Gael Clichy and Sergio Aguero, before surviving a late onslaught to hang on, after the visitors had halved the deficit.
Speaking in his post-match press conference, the Blues boss reflected: “It shows good resilience. After the game at Anfield, we were resilient.
“These players deserve support. We are going to try to play better but we need the support. I want more.
“We are aware of the problems we’ve had, [as I have been] adapting in this league.
“We are going to learn again and we are there. We won a difficult game and it will be tough for everybody with the Champions League and the FA Cup.
“It’s always important to win the games. Game by game, we will try to play as well as possible.
“The players deserve credit and my respect. I love them.”
On the subject of the red card, which will rule the Brazilian out for another four games, Guardiola added: “Ask the referee] - not me. We will play without Fernandinho.
“We try to play football. I cannot control the circumstances.”
Aguero came off the bench at half-time and produced a moment of magic to double the advantage, squeezing home from a narrow angle.
Guardiola was impressed, and explained why the Argentine had not started the game.
“Sergio helps a lot, mostly scoring goals,” he continued. “He played 90 minutes after four games out and I did not consider him playing 90 minutes again after two days.
“He helped us a lot.”
City now turn their attention to the FA Cup, which has pitted them against fellow Premier League outfit West Ham on Friday night.
Guardiola hopes his side can build a run of momentum, following Monday’s hard-fought victory.
“Friday is a final,” he stated. “We will be in or out [of the competition]. We don’t have many days to use [before the next game].
“Winning always gives you optimism and belief. We have to keep putting pressure on the rivals.
“We need to focus on our games and not think too long-term.”