The Dutch Eredivisie leaders gave up a first leg advantage to settle for a 3-3 aggregate result in Amsterdam on Wednesday.
Lucas Moura’s hat-trick cancelled out goals from Matthijs De Ligt and Hakim Ziyech to secure a final berth for Tottenham on away goals.
The defeat ended the Sons of Gods’ dreams of qualifying for their first Champions League final since 1996 and to win their fifth title in the competition.
In his reaction to the result, Kanu who was a member of the Ajax team that won the elite European tournament in 1994-95, praised the players' spirit for getting to the last-four stage.
“So close. We will always keep our head up. Proud of you boys,” Kanu wrote on Instagram.
Ajax will hope to bounce back from their Champions League exit in Sunday's league meeting against Utrecht as they aim for their first Eredivisie crown in five years.