The Champions League campaign saw Klopp deliver his first trophy as Liverpool boss after an incredible season. But a remarkable 97-point Premier League haul was still not enough to claim the club's first English league title since 1990, meaning the Reds still have more to achieve.
And 'more to achieve' is the message that Klopp has drilled into his player early in pre-season, with the German coach hoping that last season was just the start and not the pinnacle.
"He said that this morning in the meeting," Gomez told LiverpoolFC.com this week.
"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."
Liverpool have secured the signing of Dutch teenager Sepp van den Berg and are expected to also land 16-year-old Fulham prodigy Harvey Elliott, but few other new faces, if any, are likely to arrive at Anfield this summer.
Alberto Moreno and Daniel Sturridge have both been released after reaching the end of their respective contracts, but rather than replace the pair, Klopp has been tipped to make use of his existing squad and promote from within.
The versatile Gomez and James Milner are capable of playing the left-back role, while homegrown left-back Adam Lewis has a chance of making the first-team squad. Similarly, Klopp is thought to have faith in 19-year-old Rhian Brewster to replace Sturridge.