The Toffees completed a miserable run of results over the festive period with a 2-0 loss at Hull on New Year's Day, leaving them a disappointing 13th in the Barclays Premier League.
It was their fourth straight defeat and a seventh in the last nine matches, a sequence that has put Martinez in an uncomfortable position.
But club captain Jagielka insists the squad are fully behind the Spaniard and must take responsibility for changing things.
Asked if the manager's position was becoming an issue for the players, the England defender said: "We're massively behind him
I don't think it's come to that point.
"You see pundits, newspapers or social media but things haven't gone from hero to zero in the space of nine games.
"It's not a good place to be right now because if you were an honest Evertonian you wouldn't be confident in us keeping clean sheets and you wouldn't be confident in us scoring too many goals.
"That's not a good combination but we've got some good players and some good characters so we need to come to the party.
"At the end of the day we go out there to play and if we don't pick up results, the manager will take a bit of the blame but the players have to go out there and perform.
"We've got a lot to answer for and the only way we can make it up to the fans is by winning games."
The FA Cup third round draw could have been kinder to Everton, who face a testing tie against high-flying West Ham on Tuesday.
But Jagielka is still banking on an upturn in fortune.
"There's a lot of stuff for us to sort out but hopefully we can get a result in the FA Cup and that can give us some sort of confidence to take into the league," he said.
"We hope to be a bit happier after West Ham but we need to sort out our league form, which is just not good enough."
Hull started the new year in good heart, dominating proceedings and taking the points courtesy of first-half efforts from Ahmed Elmohamady and Nikica Jelavic.
That lifted them to 15th in the table, but still only two points clear of the drop zone.
Survival remains the primary objective, rather than a repeat of last year's FA Cup final.
The Tigers face Arsenal on Sunday in a repeat of May's Wembley showpiece, but Steve Bruce is battling a raft of injuries.
Michael Dawson and Mohamed Diame have been out for a number of weeks, while victory over Everton came at a physical cost.
"The disappointing thing was we've lost three or four players through the ridiculous programme over Christmas," said Bruce.
"The traveling and everything involved with it is total nonsense
We've lost three more arguably to fatigue
(Liam) Rosenior has a hamstring, (Andy) Robertson needs an ankle X-ray and Gaston Ramirez hurt his groin.
"As well as that, Abel Hernandez is physically exhausted."
Source : PA
Source: PA