The manager's contract expires this summer, and the Toffees defender does not believe his team-mates can affect the Scot's choice over whether to stay at the club
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The Scot has been in charge of the Toffees since March 2002, but his current contract is set to expire in the summer.
Moyes has opted to delay any decision on a renewal until the conclusion of 2012-13 campaign, with the Everton still in the mix for Champions League qualification.
The defender told the Daily Mirror: "We don’t feel that we have to prove anything. The manager has pretty much brought every single player in, bar one or two, so we are his players.
"He’s made the decisions that he wants to make. He has come out and said he won’t sign anything until the end of the season, which is fine with us."
Jagielka looked to have sent Everton into the FA Cup quarter-finals with a second-half header against lower-league Oldham, only for Matt Smith to net a stoppage-time equalizer to force a replay.
And the defender says any end-of-season departure for Moyes will not taint an FA Cup triumph for the five-time winners.
He continued: "At the end of the day, if we do win the FA Cup and he doesn’t sign, it will still be a fantastic feat for the players.
"We are a very close squad and we get on very well. As much as we go out there to do it for the manager, we also do it for each other as well as the fans."