Chelsea 1 Liverpool 0 (Chelsea win 2-1 on agg)

There was a point here when the heat of the battle was becoming so intolerably high the two managers had come together on the touchline and were straying dangerously close to a full-on confrontation. That clash between José Mourinho and Brendan Rodgers seemed emblematic of a night when the undercurrent of bad feeling between the two teams was never too far the surface and Diego Costa went far enough the English Football Association may feel compelled to act.

It was a breathless encounter full of incident and drama and probably encapsulated by the way Mourinho did not even see the decisive goal. As Branislav Ivanovic headed in Willian's free-kick four minutes into the first period of extra time the Chelsea manager had turned his back to the pitch to complain to the fourth official, Phil Dowd.

Mourinho's already considerable list of injustices – some credible, others much less so – has been bloated again as Chelsea were denied an obvious first-half penalty, and there were a couple more additions when Jordan Henderson and Lucas Leiva both escaped being shown second yellow cards.

Mourinho might have been close to self-combusting if Henderson had taken the game to penalties with a headed chance 111 minutes into a thrillingly spiky encounter and there is no doubt the referee, Michael Oliver, made a succession of bad mistakes. Yet Mourinho's grievances were undermined by Costa's provocation and the two incidents when his studs landed on players who were on the ground.

Costa is so accomplished in the dark arts of his trade that he managed to get away with the first even though the fourth official, Phil Dowd, was standing a few feet away. The stamp was delivered directly in front of the dugouts but contained enough disguise it was only when Emre Can went after his opponent to remonstrate that it became clear something underhand had gone on.

The video evidence was damning and the repercussions for Costa could be considerable if the FA’s disciplinary department – albeit never the easiest organisation to second-guess – rule it was intentional, with a first-against-second encounter with Manchester City to come on Saturday.

Chelsea had their own grievances later in the first half when Martin Skrtel clearly tripped Costa inside the penalty area and the referee continued the recent run of significant errors by giving the Liverpool defender the benefit of the doubt. Skrtel angrily let Costa know what he thought about him but the truth is a penalty should have been awarded.

Mourinho’s displeasure on the touchline was obvious, having initially believed along with much of the crowd that Oliver had pointed to the penalty spot, and his sense of frustration was exacerbated because those were moments when Chelsea were struggling to get control of the game.

Liverpool had continued where they left off in the first leg, passing the ball crisply and effectively and reminding us in brief passages of the slick, adventurous football they played last season. What they did not have was someone with Luis Suárez’s ability to finish off one of their chances when they were finding the same sort of gaps that Bradford had exploited at the weekend.

Philippe Coutinho's ability to run with the ball was a prominent feature and Raheem Sterling was another difficult opponent for Chelsea's defence. Steven Gerrard has benefited from reverting to a more advanced position and their wing-backs, Alberto Moreno and Lazar Markovic, operated high up the pitch to try to double up on their opponents.

That made it a difficult night at times for Kurt Zouma, Mourinho having decided the 20-year-old should partner John Terry with Gary Cahill dropped to the bench after a poor sequence of matches from the England international.

Mikel John Obi, substituted against Bradford, did not even warrant a place on the bench but it was Cahill's omission that delivered the clearest message that Mourinho was not going to tolerate his team being so generous in defence.

Zouma is a defender of rich potential but he can also look raw when facing nimble attackers and, by half-time, Chelsea were indebted to Thibaut Courtois’s goalkeeping for denying Moreno and Sterling.

Mourinho must have been startled that Simon Mignolet was less occupied in the first 45 minutes but Chelsea did start to get on top early in the second half, despite Cesc Fàbregas being hurt in an accidental collision with Terry. Mignolet has been too vulnerable too often for Liverpool this season but there were a succession of fine saves during these moments, in particular when Costa fired in a low right-foot effort that took a hefty deflection and could easily have wrong-footed him.

The studs Costa left on top of Skrtel’s foot were expertly disguised again and followed by the usual look of bewildered innocence when his opponent decided to prolong the argument.

Shortly afterwards, Mourinho could be seen complaining that the referee needed glasses for an offence by one of Liverpool’s players. Rodgers took exception and used his right arm to lever his one-time colleague away from complaining to Dowd. Mourinho flicked an arm back and the undercurrent of bad feeling was evident again when Henderson, already booked, handled the ball in a Chelsea attack without a second yellow card being brandished.

(Guardian service)