Seven-time champion Federer led 6-3 3-0 when Ukrainian Alexandr Dolgopolov withdrew with an ankle injury, while Djokovic's opponent, Martin Klizan, pulled out at 6-3 2-0 down after 40 minutes of play.
Federer later said the idea had been floated of him taking on the Serb in a practoce match to give the crowd some compensation for their disappointment.
"When I went out, I felt like there was a bit of a letdown from the crowd. They couldn't believe that it happened again, exactly the same situation," Federer said.
"When I walked up, the chairman said: 'You guys should go and play for another set and a half.' I said: 'Yeah, let me go try to find Novak.'
"I found him in the locker room. I told him, Maybe we should go out and play another set".
But it didn't happen.
"I feel for the crowd. They're there to watch good tennis, proper tennis," Federer said. "At least they see the two of us who gave it all they had. They saw other players that tried at least," he said.
Instead of the champions' clash, organisers opted to switch the women's match between former world number one Caroline Wozniacki and Hungarian Timea Babos to Centre Court.
In other men's matches, last year's runner-up, Milos Raonic, cruised through to the second round with a 7-6(5) 6-2 7-6(4) win over Germany's Jan-Lennard Struff.
The sixth seed struck 20 aces and fired the fastest serve of this year's tournament at 141 mph to seal the victory on Court One.
Spaniard David Ferrer beat 22nd seed Richard Gasquet of France 6-3 6-4 5-7 6-2 to maintain his record of always winning his first round matches at Wimbledon.
Eighth seed Dominic Thiem beat Canadian Vasek Pospisil 6-4 6-4 6-3 in an hour and 55 minutes in play on Court One. He will meet Gilles Simon of France in the second round.
Bulgarian Grigor Dimitrov moved to the second round with a 7-6(4) 6-2 6-2 win over Diego Schwartzman of Argentina.
Tenth-seeded German Alexander Zverev booked a spot in the second round with a 6-4 7-6(3) 6-3 win over Evgeny Donskoy of Russia. The 20-year-old's older brother Mischa also reached round two by beating Australian Bernard Tomic in straight sets.
The Zverevs became the first pair of seeded brothers to reach the second round in the singles at Wimbledon since Gene and Sandy Mayer in 1982.
World number 22 Albert Ramos-Vinolas beat Australian Jordan Thomson 6-4 6-4 7-6(4) to progress to the second round for the third consecutive year.
Argentina's Juan Martin Del Potro rallied to see off Australian Thanasi Kokkinakis 6-3 3-6 7-6(2) 6-4 in just over three hours.
Briton Kyle Edmund recorded his first ever Wimbledon victory with a 4-6 6-3 6-2 6-1 scoreline over compatriot Alexander Ward.
Shaky start for Kerber
Women's top seed Angelique Kerber, who opened Centre Court proceedings in the absence of title holder Serena Williams, looked far from her best but claimed a 6-4 6-4 win over American qualifier Irina Falconi.
On Court One, third seed Karolina Pliskova needed just over an hour to record a 6-1 6-4 win over Russian Evgeniya Rodina.
Seventh seed Svetlana Kuznetsova claimed a 6-3 6-2 win over Tunisian Ons Jabeur in the first round. Kuznetsova, a three-time quarter-finalist, will meet fellow Russian Ekaterina Makarova in the next round.
Fifth seed Caroline Wozniacki dropped a set but came through to beat Hungarian Timea Babos 6-4 4-6 6-1 in the first round.
World number 14 Kristina Mladenovic beat fellow Frenchwoman Pauline Parmentier 6-1 6-3 in just over an hour. The 12th seed recorded 11 aces on her way to the victory and will meet American Alison Riske in the next round.
Agnieszka Radwanska overcame a tough first set before wrapping up her match in style, claiming a 7-6(3) 6-0 victory over Jelena Jankovic.
Australian Daria Gavrilova, the 20th seed, lost to Croatian qualifier Petra Martic 6-4 2-6 10-8 in a battle that lasted for two hours and 35 minutes on Court 14.
Spaniard Garbine Muguruza launched her campaign with a convincing 6-2 6-4 win over Ekaterina Alexandrova in just over an hour. The 2015 finalist put on a fine performance, claiming nine of 11 points at the net.
Australian Arina Rodionova claimed a shock victory on her Wimbledon debut, beating 16th seed Russian Anastasia Pavlyuchenkova 3-6 7-6(8) 9-7 on Court 17. World number 166 Rodionova has reached the second round of a grand slam for the first time in her career.
American Coco Vandeweghe has reached the second round with a 7-5 6-2 win over Mona Barthel of Germany. The 24th-seeded Vandeweghe, who has teamed up with former men's champion Pat Cash, recorded an impressive tally of 30 winners to seal the victory.
