Croatia teammate Niko Kranjcar nicknamed him "a professor of football" after the remarkably self-assured debut against Serbia.
"My teammates at Inter helped me a great deal over the last few weeks and they are truly fantastic," Kovacic told Croatian media.
"Dejan Stankovic has been there for 10 years and is a real symbol, while Samir Handanovic speaks practically the same language as me and gives a lot of advice.
"After the game, the Inter director Marco Branca called me up to give his compliments on the performance. It was very nice.
"It's not easy to play from the start in a game like this, but I cancelled out the pressure thanks to the help from my more experienced teammates."