The pair won the Scudetto together with Inter Milan and today Eriksen was recalled to the Denmark squad for the first time since last year's cardiac arrest.
"I'm happy for Christian," said Conte.
"To see him again on the pitch, to play from the start, to play two games in a row. To play well with Brentford, it was special for me.
"He is an important player but also we're talking about a great person. He and his family deserve to live now in a normal situation."