The 53-year-old took over from Roberto Di Matteo in November and has since guided the club to third place in the Premier League but has faced criticism from supporters ever since he took over for comments made while managing former club Liverpool.
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"It was a great performance in the second half. We had some problems in the first half against a very good team but I'm really pleased for the players, for everyone involved," the Spaniard told ITV Sport.
"We didn't have the legs. We had to adjust and push them and in the end they deserve it because they've been working so hard the whole season. Obviously I'll be proud because it was not easy. We have been talking about this all the time. So really pleased, really proud."
Benitez's compatriot, Fernando Torres, scored Chelsea's opening goal in the final and suggested after the match that he wanted to stay and see out his contract with the club.
"I'm very happy," he said. "It was hard getting here and it was a very tough game – maybe Benfica deserved to win – but at the end the individual quality made the difference.
“The first half was not good enough at all, in any way. The intensity, the concentration. We talked about changing [at half-time] our mentality to win a final, it's a final. Maybe this would be the only chance to win a Europa League so you saw a difference in the second half."
When asked if he wanted to stay at Chelsea, Torres replied: "Yeah, sure. I signed a five-and-a-half-year contract so I hope to stay for at least this time.
"It was great for me [scoring the opening goal]. We deserved this. It's been a very difficult season with a lot of games and in the end today was a very hard game, very difficult.
"Benfica played well but, in the end, we scored from the set-piece and we prepared for this before the game. The supporters and the team deserve to get a trophy this season."