The win marked a seventh consecutive success for the Merseyside club on their own turf although it required a 93th minute winner from Seamus Coleman that flew into the Cardiff net via a mis-hit shot.

Earlier on Saturday, Gerard Deulofeu had put Everton in front at Goodison Park thanks to a lucky deflection off defender Steven Caulker, a lead which his side held for only nine minutes before Juan Cala equalised for Ole Gunnar Solskjaer's team.

Sixth placed Everton are eight points behind fourth placed Arsenal and realistically they appear to be competing with Tottenham and Manchester United for fifth place and Europa League football.

But Toffees boss Martinez has not ruled out an even more memorable finish and a place in Europe's elite club competition.

"We all believe we are capable of beating anyone and we have three big games at Goodison - against Arsenal, Manchester United and Manchester City," he said.

"We have five good away games as well. When you talk about the league, you have to answer questions about where you're going to finish. But now is the moment when, with 51 points, mathematically we can reach good spots in the league.

"There are 30 points left to play for. Are we going to get all 30? I don't think so but that has to be our target.

"It will take incredible resilience, patience and character and I think you saw that from the players today."

Solskjaer has concerns at the other end of the table as his side failed to move out of the bottom three and the Bluebirds manager was unhappy at referee Roger East's decision not to award a penalty after Wilfried Zaha fell under a challenge from Sylvain Distin.

"It was a stonewall penalty for Wilf," said Solskjaer. "I don't know how many times we have to look at us claiming a penalty and not getting it.

"It's about time we did. We've had that quite a few times since I've come here and I don't think it was because we were the away team.

"We have had stonewallers at home with Kenwyne (Jones) as well and our crowd is quite loud too. Today, it's a cert.

"He weaved his way through two, three, four defenders when Distin trips him up. But you can talk about it all day long, look at the video, that doesn't help, does it?"

One consolation for Solskjaer was the performance of David Marshall, one which Martinez claimed was as good as one will ever see from a goalkeeper.

"He's been brilliant all season, David Marshall," said Solskjaer.

"He was outstanding again today. The two goals he couldn't do anything about - the first one is a deflection, the second one a mis-hit. He was outstanding."

And Solskjaer remains defiant about his team's chances of survival, adding: "I'm definitely encouraged.

"The performance was outstanding, phenomenal effort, team spirit, they created chances and they had what you call 'cojones'.

"They've come to a difficult place and they've given Everton a good game, that's encouraging. But we sit here with no points and we need points."