Van Dijk and Gomez entered in the 69th minute of the loss at Austria's Tivoli Stadion, which saw Stevan Jovetic score a second-half brace to seal the win for the German side.
Klopp then substituted out the starting XI with 20 minutes left in the match, with Van Dijk and Gomez pairing up once again in the backline. Van Dijk had surgery in November after damaging an anterior cruciate ligament in Liverpool's 2-2 Premier League draw at Merseyside rival Everton in October. Gomez also had knee surgery to repair a tendon he damaged while training for England before their friendly against Ireland in November.
Liverpool's Premier League title defence crumbled in their absence but were able to qualify for the Champions League.
Despite the return of Van Dijk and Gomez, Jovetic was able to score in the 66th and 80th minute to deliver the win for Bertha, with Alex Oxlade-Chamberlain pulling one back minutes before full-time.
Van Dijk wrote on Twitter after the game that "285 days ago, I started on a journey back towards playing. It's hard to express how I am feeling, but it's important to me that I say I feel blessed to have had the support of so many incredible people.''