Modric, a Croatia international, said he was sorry for Rafa Benitez, sacked and replaced by Zidane last week after less than half a season in charge, but that somebody had needed to pay the price for an indifferent run of results.
Gareth Bale netted a hat-trick and Karim Benzema scored twice at a festive Bernabeu, united in hailing their hero Zidane, as third-placed Real closed to within a point of Atletico Madrid, who play at Celta Vigo later on Sunday.
Spanish and European champions Barcelona, who have a game in hand, are a point ahead of Atletico after they thrashed Granada 4-0 at the Nou Camp on Saturday.
"I am sorry for Rafa and I would like to thank him for his work, but being honest and seeing today's game I think that the change has been positive," Modric told reporters.
"When you lose there is always someone who has to pay," he added.
"You just have to compare this match with the previous ones. The team's attitude was different and hopefully we can continue in the same way."
One of the reasons Real president Florentino Perez decided to discard Benitez and promote Zidane from B team coach was the apparent breakdown in the old coach's relationship with dressing-room heavyweights such as Cristiano Ronaldo and James Rodriguez.
The change in the dynamic with Zidane at the helm was palpable on Saturday, with the players looking more determined and committed and working hard for each other in attack and defence.
"We played a lot more rapidly and we functioned as a team in the way was always should function," Modric said.
"Today we were a team from the start, up front, at the back and in the middle.
"What we did against Deportivo was to pressure higher up the pitch and win back a lot of balls and when we had possession we were very dangerous."
Real's next outing is a La Liga game at home to Sporting Gijon next weekend.
They play the first leg of their Champions League last-16 tie at AS Roma on Feb. 17.
(Writing by Iain Rogers, editing by Clare Fallon)
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