Djokovic beat Federer in the longest Wimbledon final of all time in July to claim a 16th Grand Slam title of his career.
The Serbian then needed a prolonged rest before returning to action at the Cincinnati Masters.
After receiving an opening-round bye, the world No 1 took on big-serving Sam Querrey last night.
And Djokovic fell 2-0 down early on after delivering three doubles faults in the opening game.
However, the 32-year-old quickly found his rhythm to rally to a 7-5, 6-1 victory.
And he claimed needing such a big rest after the fight against Federer made it difficult to get out of the traps.
“I made three double faults in my opening game and lost the break,” Djokovic said.
“I was quite a nervous at the start.
“I’m really glad to overcome a challenge like this and get myself going.
“That (Wimbledon final) was one of the most epic matches I’ve been a part of and probably the most demanding one from the mental perspective.
“So it really did take me some time to recharge my batteries, especially in my head. My body was fine.”
Djokovic takes on Pablo Carreno Busta in the third round tomorrow.
Carreno Busta saved a match point in his three-set win over John Isner last night.
Meanwhile, Federer also got off to winning start in Cincinnati.
The Swiss star beat Juan Ignacio Londero in a match which was heavily disrupted by rain.