"I should not have done what I did, obviously not," Mourinho told Fox Sports during Real's pre-season tour of the United States.
"The person who messed up there was me," added the Portuguese, in an interview posted on the broadcaster's website.
During a Super Cup match last season, Mourinho stole up behind Vilanova, who was assistant to Pep Guardiola at the time, and jabbed a finger in his eye.
Vilanova responded by shoving Mourinho away and although both were handed Super Cup bans by the Spanish football federation (RFEF), federation president Angel Maria Villar exonerated them last month as part of a general amnesty.
They can take their places on the bench for the first leg of the traditional season opener at Barca's Nou Camp stadium on Thursday August 23 and the return game at Real's Bernabeu arena on Wednesday August 29.
Mourinho, whose Real side ended Barcelona's three-year grip on the Spanish title last term, said his relationship with Vilanova had since been repaired.
"I work a lot with my players precisely on this, control the emotions, only think about playing and work well," he said.
"The key thing is the negative image. As Tito said a few weeks ago, the footage will be there for ever.
"There are no problems between him and me. The story is over and what needs to be done now is to make sure nothing similar happens again."
The Spanish Super Cup pits league champions Real against King's Cup winners Barca.
