"I am really very happy but the trophy is very important for the club. The name of the player and coach is less important," Sarri said after Chelsea blew away their London rivals in the second half to win 4-1.
The victory caps a season in which they finished third in the Premier League to secure a return to the Champions League before coming into this match. Despite that, Sarri has been strongly linked with a return to Italy this summer with Juventus.
"Of course the trophy is very important because we were in trouble in January and February and then we reacted.
"It is not easy to do that in the Premier League because the level is really very high.
"In the end we got into the Champions League, we played the final of the League Cup and lost on penalties to Manchester City, and in the Europa League we played 15 matches and won 12 and drew three so I think we deserved to win it."
Eden Hazard scored twice, including from the penalty spot, after Olivier Giroud and Pedro Rodriguez had netted to put the Blues in control in Azerbaijan.
Sarri added: "It is very important for me but I am really very happy for my players."
There was disappointment for Arsenal coach Unai Emery as his side suffered a bruising final defeat that also means they will miss out on the Champions League again next season for the third year running.
"We knew it was going to be difficult to take our first target," Emery said, referring to Champions League qualification.
"In the Premer League we were closer to achieving that but we lost out by one or two points to the other teams like Tottenham and Chelsea.
"The Europa League was another way. We tried and we worked, but congratulations to Chelsea. They are now better than us."
Emery had been hoping to win this competition for the fourth time after three consecutive victories with Sevilla from 2014 to 2016.
"In the first half we had possibilities, some chances to score, and didn't concede a lot to them.
"In the second half our idea was the same, to carry on our game plan, but they scored the first goal and that was very important in this match.
"They have very good players, and we played with some young players. We knew it was going to be difficult."