The contest was held over after the marathon battle between Rafael Nadal and Gilles Muller concluded late on Monday.
Djokovic was due to follow Nadal on to Court One but the Spaniard's four hours 48 minutes defeat by Muller did not finish till 8.35 local time, which meant the Serb's match could not be completed before dark.
The Serb, who had been stuck waiting for the end of that battle only to be sent home, said it would have been better to have moved his match to the, by then unused, Centre Court.
"I just think it was a wrong decision not to play us last night, because we could have played," Djokovic said.
"I think the last match on the Centre Court was done before 7pm. Having in mind that Centre Court has the roof and lights, we could have played till 11pm.
"We went to the referee's office before eight. (We were told) there were security reasons (for not moving the match). That was the only excuse... that we were getting."
On Monday, the All England Club said: "30,000 people still remained in the grounds, and therefore moving the match would have created a significant safety issue."
"Obviously I was not happy not to play last night," Djokovic continued. "We were kept for two and a half hours in the dark, in a way, without knowing what we are going to do. So you were on your toes warming up, cooling down. (The) referee's office was completely indecisive.
"It was frustrating last night. But I quickly just turned the next page and just focused on what I need to do today. I've done it in straight sets. That's all that matters."
When the match did get under way, light rain led officials to close the roof over Centre Court, but despite his frustrations Djokovic came out strongly and easily won the first set.
The second-seed took a 3-0 lead in the second but Mannarino broke back in the seventh game and took the contest to a tie-break. Both players struggled to hold serve but Djokovic won five of the last six points to triumph.
The Serb, who will face Czech Tomas Berdych in the last eight, got his nose in front with a break in the third game of the third set and never looked in danger from then on.
The only worry for Djokovic was the pain from his shoulder, which required medical treatment during the third set.
"We'll see. It has something which has been dragging back and forth for a while, but I am still managing to play," he said.
(Reporting by Simon Evans, editing by Christian Radnedge and Pritha Sarkar)
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