The 23-year-old cut a frustrated figure after being replaced in the second half of Inter's 2-0 Serie A win over Genoa on Saturday.
"I'm working very hard to improve every day," Martinez told reporters. "I want to give my best for Inter and my team-mates.
"I'm happy at Inter. We are working hard because we want to win titles to make Inter great again.
"This is what I think today. I don't know what will happen tomorrow but today I can tell you that I'm happy at Inter.
"I'm grateful to the supporters for the love they showed to me and to all the people working at Inter. This is really important for me, that's all."
Inter – who have never lost against Ukrainian opposition in all European competition – made light work of Shakhtar in their previous meeting, winning 5-0 in the Europa League semi-final in August.
Romelu Lukaku and Martinez each scored twice in that emphatic victory in Dusseldorf as they became the first Inter striker duo to hit at least 20 goals each in a single season since Adriano and Obafemi Martins in 2004-05.
Lukaku, whose 34 goals in all competitions was the best tally for a player in his first season at the club since Ronaldo 22 years ago, has already hit seven goals in six appearances in 2020-21.
Martinez scored 21 goals across all competitions for Antonio Conte's Inter last term.