Jurgen Klopp's men drew 1-1 with Manchester City in normal time at Wembley last Sunday, before being beaten 5-4 in a fiercely contested penalty shootout.
They will have another chance to do exactly that in Istanbul this week, when they take on Europa League winners Chelsea in the 2019 Super Cup final.
Liverpool will travel to Turkey fresh after a 4-1 win against Norwich on the opening day of the 2019-20 Premier League season, and Gomez is eager to banish the memory of their Wembley defeat at the start of the month.
“I think now that just made us even hungrier to get our hands on a piece of silverware again. I think that's going to be our aim this year, just to get as much silverware as possible.
“Hopefully we can do it, but it's obviously against a tough side and we know it won't be easy. We're looking forward to it.”
Despite picking up a sixth European Cup last term, there was a still a lingering sense of what might have been for Liverpool in the Premier League, as their 29-year wait for the title continued.
Klopp's men finished a single point behind City in the final standings, amassing a club-record tally of 97 while only losing one game.
Gomez is aware that Liverpool's status as Champions League winners has left them with a target on their backs, but he feels there is still "so much more" for the team to achieve in the next 12 months.
“Obviously it's a label that's given now that we achieved what we did last season," he added. "I think the main thing in our minds is that we still see ourselves as underdogs, we still see ourselves as a hungry team that hasn't achieved what we want to achieve yet.
“There's still so much more to do and to surpass what we did last season. I think the main thing is that our mindset is in the right place and whatever is said after that is not up to us.”
After the Super Cup, Liverpool will turn their attention back to the Premier League, as they take in a trip to Southampton on Saturday afternoon.