Referee Tobias Stieler has apologised after awarding a penalty for an Arturo Vidal dive in Bayern Munich's 2-0 DFB Pokal semifinal win over Werder Bremen.

Bayern settled the tie when Thomas Muller converted the spot kick in the 71st minute of the game at the Allianz Arena as they secured a place in the final.

Bayern had been leading courtesy of Muller's first-half header at the time of the incident but had come under growing pressure from the visitors, who saw an equaliser ruled out in the 61st minute when Stieler ruled that Finn Bartels had fouled David Alaba before he put the ball into his own net.

Shortly afterwards, Stieler pointed to the spot when Bremen defender Janek Sternberg challenged Vidal in the area and the Chile international jumped and fell to the ground despite the absence of any contact.

Arturo Vidal won a penalty for Bayern Munich following Janek Sternberg's challenge. A. Beier/Getty Images for FC Bayern

That allowed Bayern to end Bremen's resistance and the referee admitted after the game that he had made a costly error.

"I am sorry," Stieler told reporters after looking at the footage of his decision. "It's all happening really fast, and I was in a good position. I saw contact, but there was none."

Speaking on ARD TV following the match, Muller admitted that his teammate dived but said: "I still need to convert the penalty."

He added: "He didn't really hit him. Sternberg takes a lot of risk with that challenge, and it was a case of Arturo jumping to avoid the touch. But it was a dive. The goal counts regardless. There is no excuse for it. It shouldn't be like that -- if a similar penalty was awarded against us, I'd strike a more serious note."

Bremen CEO Thomas Eichin remained calm in his post-match interview on ARD.

"It's a dive," he said. "That's clear, but I won't reproach the ref for a decision like that. He can't always see it. Vidal waits for the contact, does not get it, but has the idea to take the foul."