The Glasgow giants, who have won the Scottish Premiership and Scottish League Cup this term, added the Scottish Cup on Saturday thanks to a 2-0 win over Motherwell at Hampden Park.
Celtic also completed a domestic sweep last season, and upon their victory in the Scottish Cup, become the first team in British football to achieve the 'double treble'.
"I'm so happy for everyone involved, players, staff, supporters. It's an incredible achievement by everyone," Rodgers told BBC Sport. "I thought we thoroughly deserved it. A mention for Motherwell, they have had a great season. I thought we could have been cleaner with passing at times... but the boys were brilliant.
"I'm very lucky to get the chance to manage the club. You can only do your best and the last couple of season have been magical. I said to the players before the game, 'this is a chance for you to make your own history, to win today, it's going to live with you, your families and the supporters forever'. It's never been done, so big applause to the players. It's a great day for everyone.
"We can be better next year. We set out to win three trophies, but I need to push them even harder next year. There are improvements we can make. We'll go away, recover and come back with big motivation in the summer."
Celtic have also enhanced their reputation as the most successful club in the Scottish Cup with their 38th title.