Deserved defeat by Aston Villa in the one English competition Roberto Mancini has yet to win merely scratched the surface of his frustrations at Manchester City. The Italian ended a fractious night claiming he has become an easy target for rival Premier League managers who cower before Sir Alex Ferguson at Old Trafford.

Mancini's anger stemmed from a touchline row with Paul Lambert, who joined Tony Pulis, David Moyes, Kenny Dalglish and Ferguson to have confronted the City manager. The Villa manager was incensed by what he viewed as Mancini's attempts to get Joe Bennett booked for a foul on Gareth Barry with an imaginary card. Lambert later dismissed the argument in order to focus on the finest result of his brief Villa reign. But the accused was in no mood to let the matter rest.

"I am tired with this manager because I didn't say anything," the City manager said. "I asked the fourth official if it was a yellow card without moving my hands. He [Lambert] comes up to me every time but after this some managers go to bigger stadiums and don't say anything. I am tired of this, very tired. I am tired with their behaviour and it's better that some managers shut up because I didn't speak with this manager. I asked the fourth official if it was a yellow card and I thought the referee had left his yellow cards in the dressing room."

When pressed, Mancini said he had no problem with Lambert in particular but managers in general. The point he made, eventually, was that few have the courage to confront Ferguson in identical circumstances.

He added: "Every time I say something, they come. After, when they go to Old Trafford, they never say anything. When other managers [at Old Trafford] talk against the referee, they always stay on the bench and say nothing. I don't know why. Maybe it's because I am Italian but I don't know the reason. There's no problem. I just don't like this type of behaviour."

The root of Mancini's latest managerial spat was not the only recurring problem for City. Again they failed to preserve a lead, again they failed to keep a clean sheet and again they failed to convince. Villa took full advantage and extra-time goals from Charles N'Zogbia and the commanding Gabriel Agbonlahor gave the visitors a victory their adventure and ultimately resilient defending merited. The visitors were indebted to Shay Given for the additional period when the former City keeper tipped over Mario Balotelli's late header on a night when the Italian scored and completed a game for the first time this season. But this was no good luck story.

City have conceded 14 goals in seven matches this season (excluding the Community Shield) and their defence was punctured twice more in extra-time when Costel Pantilimon could only parry Agbonlahor's shot and N'Zogbia pounced from close range, and again when another Agbonlahor effort deflected in off the substitute Jeremy Helan.

"This is the problem," said Mancini. "We need to work with our defenders because they don't work well in this moment. We need to work, only this. It's the fourth competition but it's the only competition that we didn't win. For this we wanted to stay in this cup because in two years we've won everything and we're missing this cup. We are so disappointed for this."

City lost Jack Rodwell to a groin injury in the warm-up but fielded a strong side that could have been trailing to a vibrant Villa display long before Balotelli opened the scoring. James Milner flicked a simple pass into the penalty area and must have been surprised himself by the freedom afforded Balotelli. The City striker had time to control, turn and beat Given convincingly before a Villa defender came close. It was his first goal since Italy's European Championship victory over Germany.

Fortune surrounded Villa's equaliser but it had been coming. A composed one-touch move led to Karim El Ahmadi releasing Andreas Weimann down the right. His low cross was spilled by Pantilimon and the loose ball struck Gareth Barry and looped into his own net. It has been a long time since Villa supporters felt inclined to sing their former captain's name in tribute and they did not miss the opportunity to revel in his misfortune.

Parity lasted all of five minutes before Ron Vlaar conceded a free-kick 20 yards from Villa's goal. The visiting captain was punished twice, first with a yellow card, then by a trademark set-piece delivery from Aleksandar Kolarov who whipped a left-foot shot over the wall and beyond the despairing grasp of Given.

Back came Villa. Agbonlahor evaded two lame challenges as he ran at the heart of the City defence before comfortably beating the unconvincing Pantilimon. The Villa striker continued to dominate City's defence in extra-time and, for all the home pressure, there was no end product in sight. "This is a massive result for us," said Lambert. "It was a huge effort. It wasn't really a spat [with Mancini]. It was nothing. I am just delighted with the win."