The 1-0 win sees Los Che reach the round of 16 - thanks to Rodrigo's first-half winner. The visitors also survived Gabriel's red card to advance at Ajax's expense.
Celades said at the final whistle: "For many it was impossible, but we have always believed in it.
"This group is fantastic, it has overcome so many difficulties. In this club there are people who work hard.
"They are the protagonists, the soccer players."