Real Madrid weren't really a counter-attacking team. It's true that compared to Barcelona they didn't treat possession as an essential, but compared to their usual opponents including the bus-parkers they were generally going forward. In the CL they were always top three in the person stats.We are all aware of the fact he broke the record with Madrid but it was based a lot on counter attacking football. He's class at coaching counter attacks.. a master at it.
In the Liga win, you're looking at possession stats of 57% and them spending 32% in the final third as opposed to Barca's 33%. They did score a lot of goals in counterattacks and at setpieces but they scored a lot of goals in other ways as well.