Marcos Alonso put the hosts ahead shortly after the break before Rashford and an own goal by Kounde gave United the lead in the knockout round first leg at Camp Nou. Raphinha then levelled for Barcelona when his cross eluded David de Gea.
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.
"I have to make the point that it's a big influence, not only on this game but on this round," Ten Hag told reporters. "You can discuss if it's in the box or outside, but definitely it's a red card.
"I asked the referee 'why' and he said 'it was outside the box and it was no foul'. The linesman and referee were in very good positions to see and we have VAR.
"It was a really bad decision and I can't understand."
Rashford said he was confused by the referee's decision.
"I don't understand why the referee thinks that I'm going down in that position," he said. "I've touched it past him and I'm one-on-one with the keeper. There's no gain for me to go down at all."
Barcelona manager Xavi Hernandez said his side should have been awarded a penalty when Fred handled a Sergi Roberto effort with the score at 2-2.
"It seems incredible to me," he said of the incident. "They said VAR had checked it."
