Federer had announced he would be retiring after the tournament and was then only fit to feature in one doubles match.
But that gave the Swiss great the opportunity to team up with Nadal, with the duo falling to a narrow and entertaining 4-6 7-6 (7-2) 11-9 loss to Jack Sock and Frances Tiafoe at O2 Arena.
That defeat marked the end of Federer's involvement in the Laver Cup, and Nadal's participation is over for this year, too.
Nadal has been dealing with an abdominal injury in the second half of this season, with the issue notably seeing him miss a Wimbledon semi-final against Nick Kyrgios.
However, the Laver Cup, announcing the Spaniard's absence from the weekend's play on Sunday (AEST), made no reference to any ailment, saying he had pulled out "for personal reasons".
Cameron Norrie took Nadal's place in the tournament.