Jota, 28, and his brother Andre Silva were killed in a car crash in northwestern Spain on July 3 last year.
Robertson said everyone has been searching for answers to Liverpool's poor season under Arne Slot following the Reds' title win last season, but there was one obvious reason.
"It is not an excuse, but what we went through in the summer no team will ever go through," said Robertson.
"I hope they never go through it (again) because the devastation we went through … football didn't matter.
"We didn't care about football for weeks. None of us wanted to train. That was the reality.
"As footballers we then of course have a duty, we have to move on, we have to keep going and we managed that.
"The Bournemouth game (the season opener at Anfield) was ridiculously emotional with all of Jots' family being there.
"I think in the 20th minute (when, to align with the forward's now-retired shirt number fans sung Jota's name) you saw a real dip in performance after that because of the emotional impact that it had on all of us."
Robertson, who won several trophies at Anfield including the league and Champions League titles during his nine-year stay, is confident the next generation will continue to deliver despite a shaky start to their careers.
Robertson believes the likes of Alexander Isak, Florian Wirtz, Jeremie Frimpong and Milos Kerkez - signed in a £450million rebuild last summer - will come good after a testing campaign in which Liverpool never came close to defending their Premier League title.
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