The Eredivisie champions had to endure a tough UEFA Champions League campaign after being drawn in Group F alongside Barcelona and Paris Saint-Germain.
However, after wrapping up third place in the group with victory over APOEL, Klaassen is eyeing compensation in the European football's second-tier competition.
"I think a place in the quarter-finals or semi-finals is realistic," the 21-year-old midfielder told De Telegraaf.
"It's a shame that we are not in the Champions League but we knew that before the game against APOEL and did what we had to do."
Klaassen has no concerns over the continued extra workload affecting Ajax's bid for Eredivisie and European success.
"We are used to playing twice a week by now," he added.
"Of course, it is a bit harder than just training, but this need not be at the expense of the domestic title."
