Chelsea were European football's great runners-up in 2008. Second in the Premier League, second in the Carling Cup, and a John Terry penalty away from becoming the capital's inaugural holders of the Champions League.

Yet in Avram Grant's single season in charge the bitter disappointment was tempered for Terry and company in knowing that they would at least be back for a crack at the European Cup the following campaign.

Three years on and after this penalty shoot-out defeat in their FA Cup fourth-round replay – following the 1-1 stalemate over 120 minutes – Carlo Ancelotti faces the prospect of taking his Chelsea project from claiming the Double in his debut year in English football to a trophyless second season and the possibility of competing only in the Europa League in 2011-12.

The Italian hinted this week that this might trigger his resignation – if he was, of course, to first dodge the bullet from Roman Abramovich – and though Chelsea go to FC Copenhagen in the Champions League on Tuesday and are only two points from fourth position an opinion is forming that they may now finish outside the top four for the first time since Abramovich walked into the club in June 2003.

Asked if he was still confident of securing a Champions League berth Ancelotti said: "I think so. We have the possibility. We were unlucky today, the FA Cup was a very important competition for us. Now we have to look forward and keep going and prepare well [for] the next game. It is not an easy moment obviously [but] we cannot be afraid to play Copenhagen and Manchester United [on Tuesday-week] — it can be a good motivation. We have to use these days to recover well – it will not be easy."

The Italian's quest to rescue the season appeared to have struggled on courtesy of Frank Lampard's 104th-minute goal after Everton had coasted through the first half and Chelsea subsequently claimed the second. When Phil Jagielka, who had the post to thank for not scoring an own goal before the break, and John Heitinga each missed a Nicolas Anelka cross, Lampard stepped in to crack the ball beyond Tim Howard.

Before this, on an afternoon in which Didier Drogba did little to silence those who have told him Fernando Torres's £50m arrival had instantly made him a Chelsea has-been, Everton had what would have been a winner chalked off in the closing moments of normal time.

Leighton Baines, who foraged successfully throughout the game down his flank, collected the ball from a free-kick and then unloaded a right-foot shot that Petr Cech could not hold. Marouane Fellaini snaffled up the rebound to finish but the officials ruled he had been offside when following in.

When extra-time moved into the final minute the prospect that Chelsea were about to imbibe a particularly bitter pill began to emerge. Baines stepped up to curl in a left-foot free-kick that meant penalties would now decide the tie.

A showdown on the spot on a Saturday in the FA Cup is surely a collectors' item. Aiming at the goal behind which Everton's travelling support howled throughout, Lampard began the shoot-out by blasting beyond Howard. Next up was Baines, who had his effort saved by Cech to the goalkeeper's left. A Drogba boot-shuffle preceded a confident finish to Howard's left and Phil Jagielka did the same with Everton's second, which he sent beyond Cech's right.

Now came the first augury of disaster for Chelsea. Nicolas Anelka followed his miss in that 2008 Champions League final, which allowed Manchester United to claim the cup, with a lazy-looking chip that Howard stopped at half-height. Mikel Arteta's placing of the next kick to the right of Cech offered relief to David Moyes and his bench as the score was now level at 2-2. When Michael Essien and John Heitinga each coolly slotted in, Ashley Cole strode up to take the side's fifth conscious that if he missed and Everton then scored the Cup holders would be knocked out.

To the delight of Moyes he scooped his penalty over Howard's bar before Phil Neville secured victory.

Ancelotti, inevitably, was then asked who precisely had chosen Cole to take what can often be the crucial kick in the shoot-out. "I decided," the manager said. "He wanted to take a penalty. Because we try in the training session and Lampard, Drogba, Anelka, Essien and Ashley Cole were the best shooters of the penalty," Ancelotti added, reeling off the five who had taken the responsibility.

What, then, of Anelka: had he been too casual when taking his? "No. In the training session he tried a lot of times to shoot and he always scored. Obviously penalties are a lottery: sometimes you can win and sometimes you can lose. It could [still] be a very good season for us. We want to stay in the Champions League and obviously reach fourth place."

It could indeed. But Ancelotti and Chelsea need to start picking up results again. Or he could be on his way in May, along with a few of this now visibly ageing team.