Jagielka has been a regular in the centre of defence since moving to Goodison Park in 2007, but Martinez claims that the 32-year-old is under the same pressure as everyone else in the squad, despite his exploits for England at the World Cup.
"I think everyone knows being captain is a massive role," the Spaniard told reporters. "You need to look after the rest of the players but it doesn't guarantee you anything in that respect.
"Phil will be a very important player for us but no-one has playing guaranteed, that's for sure.
"With Phil, like any player who comes from the World Cup, you are, of course, going to need a period to get back to your best."
Everton continue their search for a first win of the season against West Bromwich Albion on Saturday afternoon.