Cristiano Ronaldo struck both goals for the 2-1 win, but Carvajal preferred to offer some overdue praise to Modric.
"Modric is a fundamental player for us. He brings a guarantee in the middle of the park," he said.
"I hope that he will be with us at this level for many years to come.
"Cristiano had a good game. He took the first goal very well with a good shot and then took the chance towards the end.
"The important thing for us is that we went on to win the game in the final moments."