Goals from Juan Mata and Raul Meireles saw the Blues past Birmingham in their FA Cup fifth round replay but the Italian confirmed the league is his priority.
He told the Daily Mirror: "We have to play Champions League next season. For us it's vital to finish fourth. That is the target.
"It's not about me. It's about these players, this club. The club is bigger than me, the previous managers, the future managers.
"Players win the games for you, but we have to perform and achieve targets.
"Only time will tell how difficult or easy it will be. We don't like where we are in the table, and it'll be very tough to achieve what we want to achieve.
"But we have a duty to try. We have good players and we have a duty to try that."
Chelsea had a star-studded bench for the cup clash at St. Andrews including John Terry, making his return to action after undergoing knee surgery towards the end of last month.
Di Matteo explained: "He couldn't have played the whole game. We just have to build him up to play. It's an early comeback, yes. We have a good medical department."