Having fought off big-money bids for the stylish Stones last year, Martinez also quelled speculation that Jagielka could leave the club by the end of the month.
The England centre back is reportedly a target for the cash-rich Chinese Super League where the transfer window closes on Feb.26, but Martinez said the 33-year-old was going nowhere.
"We're not in a situation to lose players. Jagielka is our club captain and has been great in the last two games," the Spaniard told reporters on Thursday.
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Martinez also refused to rule out a top-four finish for Everton despite the club lying 12 points adrift of the Champions League and said he understood Romelu Lukaku's frustration with their league position.
The Belgian striker had said on Wednesday that the team needed to show more "nastiness" to swing results in their favour, but Martinez insisted that progress was being made despite the club sitting in eighth place in the table.
"We don't try to hide the fact we want to reach the top four. That won't happen overnight but we are giving big roles to young players," Martinez added.
"Romelu accepts that challenge and that we need to become better. This is probably the most open league that I've been involved in over seven seasons.
"What's important is the type of momentum that we've got now. The answer is very much how strong we can be in the final third of the season."
Martinez said new 13.5 million pounds signing Oumar Niasse could make his debut, probably off the bench.
West Brom, who have slipped to 14th place in the table, travel to Everton hoping to register a first league win since Jan.2 .
(Reporting by Simon Jennings in Bengaluru, editing by Mitch Phillips)
