It was yet another frustrating performance from the Sky Blues, who dominated the opening period with sharp passing and intelligent movement, only to allow Everton a route back into the match after ceding the initiative.
Their away form is now a serious concern and a threat to their hopes of silverware this season.
However, a 2-1 deficit going into the home leg means City will still feel they have an excellent chance of making it to the final at Wembley at the end of February.
Their form at the Etihad has been sensational again this season. They have the best home record in the Premier League, having collected 24 points from their 10 games, scoring a remarkable 29 goals in that period.
It may not have been the result City wanted, and their performance and mentality was a cause for concern, but they are by no means out of this tie.
“If you lose 2-1 playing away, if you are not able to win 1-0 at home it’s because you don’t deserve to continue,” Pellegrini said afterwards.
“I trust absolutely what we can do in that game and I hope now we have some time to recover some players and do what we must do.”
There are 90 min left and we've got to turn it around. With your support in the home leg, we can make it to the finals. C'mon, City!— Sergio Kun Aguero (@aguerosergiokun) January 6, 2016
There were a number of underwhelming performances in the City team, with both Kevin De Bruyne and David Silva, usually their two most creative players, spending much of the match on the periphery and unable to influence the game.
De Bruyne’s form away from home is becoming a concern. Whereas at the Etihad he is constantly involved and regularly creating and scoring chances, he is less impactful away from home.
Ramiro Funes Mori's goal just before half-time changed the match. The Everton fans were in frustrated mood when City were in the ascendency. Their poor run of league form, which had seen them win just three of 13 coming into the match, was a cause for concern in the home stands. The fans' negativity was transmitting to the players.
But the Argentinian’s goal lifted everybody, and Everton began the second half on the front foot. There was more than a hint of offside, but the referee, Robert Madley, didn’t think Romelu Lukaku was interfering with play, despite being in Willy Caballero’s line of vision.
City’s luck appeared out when substitute Jesus Navas was denied what looked a blatant penalty.
The Spaniard equalised for City with his first goal of the season, but it was cancelled out moments later by Romelu Lukaku’s header.
Pellegrini, understandably, was unhappy with the decisions. “I think we didn’t deserve to lose,” he said. “Especially when you have two very important plays, the first goal of Everton is absolutely offside—Lukaku is one metre in front of Willy Caballero and he makes the movement—and after that the clear penalty on Jesus Navas in the second half that can change the score.
“But the referee didn’t whistle for both actions. We lost 2-1. I think it is a bad result. But we just have to win at home 1-0 so I think we are able to play the final of the Capital One Cup.”
City’s away form is a serious threat to their ambitions this season. Pellegrini looks almost certain to be replaced this summer, and for his time at the club to be viewed as a success, he needs to win trophies.
To finish a second consecutive season empty-handed, with the quality he has at his disposal, would mean his three-year tenure going down as underwhelming.
Given how well it started and the quality of much of the football his side has produced, it would be a huge disappointment.
They’re not out of this semi-final just yet, though. Their home form is excellent and could save them.
Rob Pollard is Bleacher Report's lead Manchester City correspondent and will be following the club from a Manchester base throughout the 2015/16 season. All quotes were obtained firsthand unless otherwise noted. Follow him on Twitter @RobPollard_.