The English official took charge of the European decider in which the Spanish giants beat rivals Atletico Madrid in a penalty shootout after drawing 1-1 in normal time.
After appearing to mock Pepe when he went down holding his head following a collision from Yannick Ferreira Carrasco, Clattenburg had another run-in with the centre-back when he awarded a penalty for a foul on Fernando Torres.
"Everyone always asks about the incident in the 2016 Champions League final when I did that thing with my tongue as he was rolling around on the floor, play-acting,” he wrote in The Daily Mail. "In my head I was thinking: 'How soft are you for a big man?'
"He did it twice in that game, trying to get an Atletico Madrid player sent off. Another referee might have fallen for it but I'd done my homework and, while you should try not to pre-judge, I knew exactly what his mentality was like and I needed that knowledge to handle him.
"He was another player you just couldn't trust. A game could be easy and straightforward then he would do something sly.
"In that final Real Madrid went 1-0 up in the first half but the goal was slightly offside and we realised at half-time — it was a hard call and my assistant missed it.
"I gave Atletico a penalty early in the second half when Pepe fouled Fernando Torres. Pepe was furious and said to me in perfect English: 'Never a penalty, Mark.' I said to him: 'Your first goal shouldn't have stood.' It shut him up.
"People might think that sounds odd, because two wrongs don't make a right and referees don't think like that, but players do. I knew by saying that to him it would make him more accepting of the situation, but he was a wind-up merchant and not fun to referee one bit, you had to be on your guard constantly."
Madrid's Champions League triumph that year was the first of three consecutive European titles they lifted during Zinedine Zidane's first spell in charge of the club.