Hiddink, who arrived in February, now returns to coaching Russia full-time, and the 2-1 defeat of Everton was a fitting finale to a successful spell in charge after replacing Luiz Felipe Scolari mid-way through the season.
Goals from Didier Drogba and Frank Lampard earned Chelsea victory after Louis Saha had put Everton ahead with just 25 seconds on the clock - the fastest goal in FA Cup final history.
Hiddink said: "We were very tough and the team has showed after a setback they react always, which is what I like.
"I loved it so much, I enjoyed it so much working with big stars but they knew what it's all about. They showed in the Premier League and Champions League and today, a lot of character."
Asked to compare the win with his other successes, Hiddink added: "It was one of the biggest, a big achievement, winning in the Mecca of world football, the FA Cup is something you cannot believe.
"We have worked so hard since February and I respect these guys very much.
"We had some wonderful performances in the Premier League and also in the Champion League and this is the highlight, to win the FA Cup."
Everton manager David Moyes had no complaints about the result.
He said: "Chelsea were the better team on the day. I thought we were having our best spell when they got their goal from Frank Lampard. He's a big player and he scores goals, and that's what he did.
"The margins were very narrow in terms of the result but there were bigger margins on the field."
Moyes praised the efforts of his players, however, saying: "I've got to give them credit. Last year was a semi-final, this year a final. Whether we won today or whether we hadn't it was progress for us."
