Jurgen Klopp's men pushed the champions all the way last term but ultimately missed out on the Premier League trophy by a single point, after a dramatic finale.
City held their nerve on the final day of the campaign to reach a tally of 98 points, one more than the Reds' haul of 97, which was the highest total ever amassed by a second-placed side in the competition's history.
Despite more domestic heartbreak, Liverpool did manage to win a sixth European Cup, beating Tottenham 2-0 in Madrid's showpiece final.
Gomez, who racked up 25 appearances for the club across all competitions despite an unlucky run of injuries, admitted the squad still has plenty of room for improvement when asked if there is a sense of unfinished business in the dressing room.
"Definitely. He [Klopp] said that this morning in the meeting," he told the club's official website.
"We can be happy and proud of the achievement but we've got so much more work to do and so many ways to improve as well.
"The Premier League was so close and I think that's all the motivation we need, that we were so close but so far at the same time in the fact that we didn't get it.
"It's something we want to get this year and to do so we can't get complacent or dwell on what happened last season, we have to hit the ground running again now."
The Reds get their pre-season campaign underway with a trip to Tranmere on Thursday, before heading to Valley Parade to face Bradford City three days later.
Gomez partnered Virgil van Dijk in the heart of the defence before he was sidelined in February and was often deployed as a full-back upon his return to action.
The 22-year-old is prepared to give his all to the Liverpool cause regardless of his position next season, as he added: "I've played a number of positions over the years I've been here.
"I like to excel in one and nail that spot but I'm happy to play wherever for the team and the manager.
"It's just about development in whatever way I can and doing all the extra bits I can to develop off the pitch as well as on it. Hopefully, things fall into place.
"This is my fifth season now and I've had a lot of experience at the club and learned a lot here. But I'm still so young, I've got so much left to learn. I've got to keep developing, keep progressing and stay hungry."