United remain in four competitions this season after earning a 2-1 victory in their Europa League playoff second leg to knock out the Spanish side 4-3 on aggregate.
Ten Hag was furious in the second half when Rashford went down under a challenge from last-man Kounde but referee Maurizio Mariani waved away claims for a foul and VAR backed the decision. Barcelona equalised soon after.
Dutchman Ten Hag was on the cusp of becoming the first Manchester United manager since the great Alex Ferguson in 2009 to win 10 successive games as his side led 1-0 at Selhurst Park in the 91st minute.
Manchester United manager Erik ten Hag said Cristiano Ronaldo's goal in Thursday's 3-0 Europa League win over Sheriff Tiraspol was a fitting prize for his perseverance after the Portuguese forward returned to the team following disciplinary issues.
Ajax reached UEFA Champions League quarter finals for the first time since 2003.