The England international, who is expected to be out for up to six weeks, claimed the injury is "not too serious".
SunSport exclusively revealed that Gomez has suffered a fracture leg and is set to miss the team's festive fixtures.
The 21-year-old was carried off the pitch on a stretcher after a heavy challenge from Ben Mee during Liverpool's win over Burnley.
But the centre-back vowed to come back stronger as he thanked his fans for their support.
In a video posted to Liverpool's Twitter page, he said: "I just wanted to say thank you to you all for your kind wishes and well-wishes.
"Obviously I'm gutted to have picked up the injury, but thankfully it's not too serious and one that I can definitely be back stronger from.
"I'll do my best to come back as quick as possible and hopefully be back with you guys soon, so thank you."
Speaking on the club website, Klopp added: "It's just a shame for the boy [and] for us of course as well.
"He was in outstanding shape. He helped us a lot, especially because we could make these changes with Trent [Alexander-Arnold] and Joe.
"That was really important because Trent is still a young boy and we cannot push them through 20 games in a row."
And the Reds boss confirmed that he is only expected to be out of action for six weeks.
He added: "I would say it is a bit of luck because it could have been worse. So six weeks for us is massive, I can't even count the games we have in that period.
"But it means as well that he will be back for a big part of the season still and that's good."
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