It is the second time they have won the competition, following their success in 2013, and Sarri has praised his team for their bravery in taking risks.
"My feeling at the end of the first half was that the match was very difficult," Sarri told Chelsea's official website.
"It was our 64th match of the season and it was hot on the pitch, very difficult to play physically. My feeling from the bench was that we were trying to manage the result. At half-time I asked my players to play with more courage, even if it meant risking to lose.
"I wanted my team to move the ball better, and the players did it very well in the second half. We played very good football against a very difficult opponent, who are dangerous in the offensive phase and from counter-attacks. We played very good football and the match was good also for the fans I think."
Chelsea's triumph in Baku, Azerbaijan, was a landmark moment for Sarri, who crowned his debut season in English football with the first major trophy of his managerial career.
But having already guided his side to a third-place finish in the Premier League the Italian insisted the team's collective success comes first and foremost.
"I am very happy, but the front of the shirt is very important – the trophy is very important for the club," Sarri added.
"The back of the shirt, the names of the players and the coach, is less important. Of course the trophy is very important for us and for me. Our feeling was we deserved to win."