Four-time European Cup winners and one of only three clubs - Juventus and Bayern Munich are the others - to win the trio of major UEFA club competitions, Ajax remain one of the game's most famous names.
However, it is 17 years since their last European triumph and when Ajax take on Manchester United in the Europa League tomorrow, they do so in the knowledge it is likely to be a long time before they repeat it such is the vast disparity in income between clubs in Holland and those in the big five nations.
The Dutch TV contract is a tenth of the £1billion plus deal negotiated by the Premier League, a figure that is only set to increase as the years go on.
Ajax's turnover of £100million is a third of United's, leading to the almost inevitable exit of all their top players even though they remain the 16th best-supported team in Europe.
"You just have to look at the facts, including the difference in turnover between the two clubs and the revenue from TV contracts," said De Boer.
"It is very big and we lose players to big leagues, so it is up to us to make sure there is a surprise every now and then."
A number of Ajax players are being coveted by Europe's major clubs.
Denmark playmaker Christian Eriksen is at the top of the list and De Boer accepts tomorrow night's game offers another chance for him to shine.
However, the Ajax boss has a word of advice for Eriksen, who celebrated his 20th birthday yesterday.
"Christian is a smart kid," he said.
"Of course maybe he will play for a big team like Manchester United in the future. But I think he wants to show what he is capable of in this kind of team.
"It would be better for him to stay until he was 25 because you learn a lot in the Netherlands.
"If you leave afterwards you are a more stable player and ready to play in the big leagues."
One player has moved from Ajax to the Premier League and made an impact is Luis Suarez.
And De Boer admitted today the Uruguayan is capable of "some stupid things".
Suarez brought shame on Liverpool last weekend when he refused to shake Patrice Evra's hand ahead of the Premier League defeat at United.
The South American was eventually forced into an apology after Reds managing director Ian Ayre said Suarez had misled the club about his intentions.
It is the latest in a long line of disciplinary woes for Suarez, who only last season was banned for seven matches by the Dutch FA for biting PSV Eindhoven's Otman Bakkal while playing for Ajax.
De Boer was assistant to Martin Jol at the time of the incident, in November 2010, but has since assumed full control at Ajax and sanctioned Suarez's £22.7million departure for Liverpool in January last year.
"Luis as a winner," said De Boer. "Outside the pitch he's a fantastic player and person.
"In the game he does everything to win but sometimes he does some stupid things.
"I don't really know the details of what happened in that (Saturday's) game so I can't comment.
"But I don't think it was very smart that he didn't shake Evra's hand because it puts more attention on everything."