The Premier League leaders saw their four-pronged trophy bid ended with a 3-2 defeat to rivals Manchester United in Sunday's thrilling FA Cup third-round showdown at the Etihad Stadium.
However, City at least emerged from the contest with their heads held high having fought back from a 3-0 deficit with 10 men following skipper Vincent Kompany's 12th-minute dismissal.
And goalkeeping understudy Pantilimon, who was handed a rare start ahead of Joe Hart, insists their self-belief has not been dented because of the way they fought back.
"It has not damaged our confidence," he said.
"It was an interesting game, but losing a player after 10 minutes is not normal. It was a foul but a normal foul and not a direct red card.
"We were surprised that the referee gave a red card after 10 minutes.
"At this level it is not normal and when you play a team like United it is important you have 11 men.
"But this is football and anything can happen. In the second half we played better, scored two goals and had a chance to get the draw."
City have appealed against Kompany's red card and will discover on Tuesday whether they have been successful.
At present, the Belgium international will be missing for their next four matches having already been sent off once this season, meaning he would miss both legs of the League Cup semi as well as league matches against Wigan and Tottenham.
Having been selected in goal for City's domestic cup games, Pantilimon hopes to have done enough to keep his place to face Kenny Dalglish's team.
"The manager decides which 11 go on the pitch and I hope to be in there," he said.
"We have both (he and Hart) trained very well, and train for the team, to win trophies.
"The team is very good and we all want to be in this team."
Meanwhile, Craig Bellamy says Liverpool will be out for revenge against his former club following their recent 3-0 defeat to City in the league.
"For me, I didn't believe the 3-0 scoreline was quite correct and this is not just me with my Liverpool head on, but if I was watching the game as a neutral we had 66 percent of possession, which is a lot for an away side, especially against a team of Man City's calibre.
"It was all about taking opportunities. Pepe (Reina) made a mistake for the first goal but the other goals came from a corner and a penalty.
"We were knocking on the door. Stewart (Downing) had a great chance and in the second half we had one or two chances we could have made more of.
"It's a two-legged match and we have to make sure we are still in the tie. We have the second leg at Anfield and this club knows all about two-legged games, so if we can get it back to Anfield still very much in the tie we will have a great chance of getting to Wembley.
"This club is used to getting to semi-finals and finals and all we can do is give it our best and see where it takes us."
Downing has returned to training following his arrest by police on suspicion of assaulting his ex-girlfriend, however his participation is in doubt. Luis Suarez serves the third game of an eight-match ban.