The Russian side were largely second-best in Tuesday's Group E contest at the Otkrytiye Arena, showing little attacking ambition.
But, having been given something to cling to when Fernando's free-kick opened the scoring, they ultimately settled for a solid point following Philippe Coutinho's leveller.
And Carrera revealed that advice from Italian countryman Conte played a part in the result.
"During the conversation we talked about Liverpool for just a couple of minutes," he said.
"We more discussed the situation in our teams, personal affairs, vacation, but what he said about the British, I needed."
Carrera added: "We played a great game against a very good team. I don't have any complaints about my team's performance.
"I just want to praise everyone. Am I happy with the result? Yes, we got a draw against a very good team."
He rejected the chance to join Conte at Chelsea in order to pursue his own managerial career in Russia.