The Eredivisie outfit open their group campaign against Paris Saint-Germain tomorrow night, before taking on Barcelona and APOEL.
However, having lost players such as Daley Blind and Siem de Jong during the summer to Manchester United and Newcastle United respectively, De Boer has admitted that the departure of such experience will have hampered his side's chances of progressing.
"We just talk about surviving the winter in the Champions League, and not about winning it yet. Getting that far would already be a success for us," he told reporters.
"Often experience makes the difference and the players who have the experience of last year, they have already left for those big leagues. That is what happens at Ajax every year, so its hard to take the next step up, but we hope it will happen in the future."
Ajax have won the competition four times, the last of which came back in 1995.