The forwards have been rumored not to get along very well, but combined to great effect in the Liga clash, with each creating and scoring the Blaugrana's goals.
"The three goals were between Messi and me. I'm happy to participate directly with him on so many," the 31-year-old told Canal+.
Stand-in coach Jordi Roura added that the two players have a perfectly good relationship, despite rumors to the contrary over the years.
"People have always talked about this, but it seems absurd to me," the 45-year-old told reporters. "Currently their relationship is the same as always, very good. I see no significance.
"I always said that Villa is very important for us and would have his moments. He plays good matches and scores."