The hosts were leading 2-0 at Anfield thanks to goals from Sadio Mane and Mohamed Salah when Scotland defender Roberston lost his footing inside his own half during Sunday's game.
Maurizio Sarri's side could not take advantage, however, and the Reds hung o to the lead to return to the top of the Premier League table.
Afterwards, Klopp told a press conference: "By the way, on this point, we can finally close the slipping book. Robbo slipped and nothing happened, so it’s not a Liverpool thing. Done."
Liverpool had briefly dropped into second place following Manchester City's 3-1 win against Crystal Palace earlier on Sunday, but stormed back to the summit with a victory sealed by a goal of the season contender from Salah.
The Egypt international collected the ball on the right touchline before cutting inside and crashing an unstoppable drive into the top corner, just two minutes after Mane had given the hosts the lead.
The result helped finally vanquish memories of the corresponding fixture five years ago this month, when former skipper Gerrard lost his footing with the game finely poised at 0-0 to allowed Blues striker Demba Ba to race away and score. Chelsea went on to win 2-0.
It proved to be the pivotal result in that season's title race, depriving Liverpool of their advantage at the league summit and allowing City to seize the initative in the final two weeks.
There are few surviving members of that squad within the current Liverpool team, though, and Virgil van Dijk insists it was not on the minds of his team-mates this time around.
“Five years ago didn’t matter today," he told Sky Sports. "They were very disappointed back then but today was a very different game.
"We showed great things during the game and we are very happy with the three points."
Liverpool lead the table by two point with four games left to play - but champions City remain in pole position to retain their crown as they have a game in hand over Klopp's Reds.