Van Dijk missed most of the 2020-21 season due to an ACL injury, while Gomez was out for a similar length with a knee injury.
The pair were both second-half substitutes in Thursday’s defeat, where Sadio Mane, Takumi Minamino and Alex Oxlade-Chamberlain scored.
“It was a nice feeling,” Klopp said.
“Started immediately well and usually we all know that the fourth goal is a clear situation which saw and defend well. But that’s it.
“I’m not sure, 260-something days for Virg and not much less for Joe they didn’t play football, so it’s nice to have them back. It was the first step, really important.”
The Netherlands international, who was integral to Liverpool’s breakthrough Premier League triumph in 2019-20, tweeted his delight.
“285 days ago, I started on a journey back towards playing,” van Dijk wrote.
“Its hard to express how I am feeling, but its important to me that I say I feel blessed to have had the support of so many incredible people. The surgeon, my physios, coaches and staff who have been with me in my corner since day one.
“My teammates for giving me energy and keeping my head up. The fans for their love, support and encouragement. And most of all, my family because without them, Id be nothing. Thank you. The work doesnt stop now. Its only just starting. We keep going!”