Serbia knew a win over Slovenia would secure them second place in Group C behind group winners Italy.
The 29-year-old is gutted he will not get to represent his country at the European Championship.
"I took responsibility and I am aware of the consequences of a poorly executed penalty," Vidic told Blic Sport.
"It was agreed that I [would take it], but I wanted to take responsibility. I will bear the consequences of missed penalties.
"If I had scored, the game would [have flowed on an] entirely different course.
"I'm sorry that I will never play at the European Championships because the following qualifications [are too far away]."