Madrid lifted the trophy after a narrow 3-2 win over their Spanish counterparts in what was a very tight affair.
Zidane admitted there was nothing to choose between the two sides, but thinks that Sergio Ramos proved the be the difference.
"You have to congratulate Sevilla on their great performance," he said.
"Sometimes to play a great game it takes two sides and today we saw just that. In the end we won, but Sevilla were very good.
"Sergio Ramos is our captain, an important player and he's always there to earn us the trophy. There were no special instructions for him. With a player like Sergio, he's always been the difference. We've seen it before. He's grown as a player, too. In this final he was there just where he needed to be".
At the end of normal-time, it looked like Sevilla were going to be lifting the trophy, having led 2-1 going into the dying stages of the game. However, Ramos scored a last-gasp equaliser to take the match into extra-time.
In extra-time, it then seemed as though the match was going to penalties, but Madrid found an unlikely hero in Dani Carvajal who scored will a wonderful finish, scoring with the outside of his right boot in the 119th minute.