The pair won the Scudetto with Inter this past season before Conte's resignation.
"It's clear that in Milan, Conte slowly instilled his vision of football in us, making us understand how to behave on the pitch," said Skriniar.
“In the first place, he influenced us with his winning mentality. He played a significant role in these successes and in my growth, like [Luciano] Spalletti did before him."
He added: “Inter are a beautiful showcase, you play in important games in front of many people. But behind all this, there must be the effort and work of the player.
“I think this is my case, everyone is always the engine of their own happiness."