Sam Allardyce described West Ham's penalty shootout victory over 10-man Everton as a fine advertisement for the FA Cup as goalkeeper Adrian's spot-kick sealed victory on a dramatic night at Upton Park.

Enner Valencia gave West Ham the lead with a clinical striker's finish six minutes into the second half, but Kevin Mirallas' sweetly-struck free-kick forced extra-time.

Romelu Lukaku slotted home from close range to edge Everton ahead, but substitute Carlton Cole needed just 100 seconds after coming to notch West Ham's equalizer and the game went to penalties.

Normal time, extra-time and nine rounds of penalties could not separate the two sides and West Ham needed the heroics of Adrian to progress to the fourth round for the first time in Allaryce's tenure in east London.

Adrian stepped up, after Everton goalkeeper Joel Robles had blasted his penalty against the crossbar, to score the winning spot-kick and send the Hammers through and Allardyce felt the game was a great advert for the oldest domestic cup competition in football.

"It was an unbelievable match, wasn't it? You can't say the FA Cup has died after that, not with that entertainment value," Allardyce said on BT Sport.

"I thought today had absolutely everything a cup tie should have – a little bit of controversy, some great play, chances missed, some great goalkeeping and some very good goals."

Match-winner Adrian was thrilled to secure West Ham a fourth-round date with League One side Bristol City.

"It was the most unbelievable game, for the fans I feel so really happy," he said.

"I was relaxed and quiet when I striked the penalty and we got the victory and keep going in the FA Cup."

Everton regrouped well after Aiden McGeady's second-half dismissal and manager Roberto Martinez felt that the Toffees did not deserve to bow out of the competition.

"I thought we were the better side," the former Wigan boss said.

"We created really, really good opportunities, probably we should have taken one or two before the one we scored.

"But in terms of the performance and the character and the phases of good football we showed, I couldn't be prouder.

"Sometimes in football you feel you are going to get what you deserve but clearly today we were unfortunate in the penalty shootout where it is a bit of a lottery."