"I wish him all the best and I hope he recovers quickly so we see him back on the courts. He could have won the match at the end. Obviously, he was the better player, so I definitely got a bit lucky," added Federer.
Nadal will next meet Swiss Stan Wawrinka at 12 am (IST) on 1 November.
Djokovic will face the Czech Republic's Tomas Berdych on Wednesday for a semi-final spot.
Djokovic advanced to the quarter-finals at Wimbledon after beating Mannarino 6-2, 7-6 (5), 6-4.
Djokovic defeated his Latvian rival 6-4, 6-1, 7-6 (2) in two hours and 11 minutes.
Mannarino advanced to the third round of the tournament after stunning Tsonga.
