Jagielka expects further improvements under Martinez
The Spaniard arrived at Goodison Park last June as David Moyes' replacement and guided Everton to fifth place in the Premier League thanks to a record points total.
Everton's captain made 26 league appearances at the heart of defence in 2013-14, continuing his partnership with Sylvain Distin and also forging a new one with John Stones.
Jagielka and his team-mates will now be playing European football again after four years out of continental competition and it is a challenge that the 31-year-ols is relishing.
"It has been brilliant playing under Roberto," he is quoted as saying in the Liverpool Echo. "Getting the record points total gives us something to try and beat next year.
"We should be even stronger because we know what to expect from the manager and his staff, and he knows what to expect from us.
"I think it is going to be really exciting moving into next season. We have missed European football, we are desperate to play it again.
"I am sure the fans are excited to get out and about, and we are looking forward to hearing and seeing them all over Europe."
Jagielka's consistent form for Everton under Martinez has seen him establish himself as part of England's first-choice centre-half pairing with Gary Cahill as the duo prepare for this year's FIFA World Cup in Brazil.