The Dutch giants are four times European champions but have not made it out of the group stages in this competition since 2005-06.
After a strong start to the campaign, hopes are high they can buck that trend this season, with them set to face Bayern Munich in Group E.
However, second place is up for grabs with Benfica and Wednesday's opponents AEK Athens on the agenda.
Blind's father, Danny, was in charge of Ajax when they last made the last-16, while he also captained them to glory in 1995.
The defender, who returned to his boyhood club in the summer after four years with Manchester United, says he is confident his side are ready for the task that awaits.
"The Champions League is very popular," says Blind. "The expectation is great, because we are not in the strongest pool.
"But of course it is not that we just finish second behind the favourite Bayern Munich. Benfica has also performed well in Europe in recent years."
When quizzed on their hopes of making it through to the last 16, he replied: "That is too long ago, but it also indicates how difficult it is. We will do everything we can to make this happen again."