Djokovic was furious when he was denied a break of serve in the seventh game of the fourth set on Centre Court when the ball bounced twice before Edmund hit what was ruled a winner.
But the Serb managed to refocus after a lengthy complaint to umpire Jake Garner and eventually secured the break that sealed his 4-6, 6-3, 6-2, 6-4 victory on Centre Court.
"I was 100 percent convinced it was a double bounce in the fourth set, but anyone can make a mistake," Djokovic said.
"It was an important point. I asked the chair umpire how is it possible he plays that shot if it didn't bounce twice. It didn't make sense.
"I had to stay mentally tough, the next game was tough. I'm just glad to overcome this challenge in four sets."
Djokovic plays Russian world number 40 Karen Khachanov for a place in the quarter-finals on Monday. Former world number one Djokovic, who won Wimbledon in 2011, 2014 and 2015, has ended Britain's challenge at this year's tournament, with Edmund the last of the 12 home players in the singles.
Djokovic is into the last 16 of a major for the 44th time to take him second on the all-time list.
"It was tough, Edmund is playing really well. The forehand we know is a big weapon. Not an ideal situation for me but somehow managed to come back," Djokovic added.
"I am looking forward to a second week of a Slam. I have been playing these Wimbledon courts for a decade.
"I have wonderful memories of Centre Court and Court one and I'm looking forward to competing some more."