Muhamed Besic says he was proud to be awarded a new contract and wants to prove it was the right decision for the club.
Besic was handed a new five-and-a-half deal in February after holding down a place in Martinez's side throughout January following a difficult start to the season.
The 23-year-old Bosnian international joined the Toffees from Hungarian side Ferencvaros two years ago and featured 31 times in all competitions for the club in his debut campaign.
However, injuries limited his involvement in the first half of the current season, but after a return to fitness and surge of good form which saw him named the club's player of the month for January, he was rewarded with a new long-term deal.
The midfielder expressed his gratitude and pride at having his stay at Goodison Park extended, and insisted he cannot wait to repay the club's faith in him.
Besic told the Echo: "I first heard about it [the offer] two or three weeks before and it went fast. When I heard from my agents, I just said: ‘Yeah, it’s clear that I will stay here’. That was it.
"I was really proud because after one-and-a-half seasons and, to be fair, I didn’t play so many games in that time because I had a lot of injuries in the beginning, I needed to get used to the league.
"Then I played and I’ve had more injuries - and yet still they trust me. It makes me want to repay them."
Besic's progress in January was hampered by another spell on the sidelines which saw him miss the entirety of February, but since his latest return he has featured in each of the club's last three matches, starting the 2-0 home defeat to Arsenal.
He will be hoping for further chances to stake a claim for a regular starting spot in the remaining weeks of the current campaign, with the FA Cup semi-final at Wembley likely in his thoughts.