Jurgen Klopp says Liverpool's owners "expect me to sort it out" when asked if he feared going the same way as compatriot Thomas Tuchel.
Klopp's fellow German coach was dismissed by Chelsea on Wednesday, with new Blues owner Todd Boehly cutting ties with the former Paris Saint-Germain boss in the wake of Tuesday's 1-0 defeat to Dinamo Zagreb in the Champions League.
That was Tuchel's 100th match in charge of Chelsea in all competitions. In his 18 months at the helm, he guided the Blues to a Champions League success, a Super Cup triumph and Club World Cup glory, as well as three domestic finals.
Chelsea failed to win any of those three domestic finals, with two of them coming as penalty shoot-out losses to Klopp's Liverpool last season.
The Reds, meanwhile, have hardly enjoyed a strong start to the new campaign. A 9-0 hammering of Bournemouth aside, Liverpool have looked a shadow of their best, and were thrashed 4-1 by Napoli in their opening Champions League match on Wednesday.
It was the heaviest defeat suffered by an English side in their Champions League opener since Arsenal lost 3-0 to Inter in 2003, while it also marked Liverpool's joint-worst loss in the competition.
Yet asked if he was worried for his future, Klopp – who has been at Anfield since 2015 – told reporters: "Not really, but who knows? The difference [between us and Chelsea] is we have different kinds of owners.
"Ours are calm and expect me to sort it and not think someone else will."
Klopp has plenty of goodwill in the bank, given the enormous success he has enjoyed at Liverpool, taking the Reds to three Champions League finals, and winning one in 2019, as well as their maiden Premier League title (2020) and winning both of England's domestic cups this year.
Jamie Carragher, who helped Liverpool win the Champions League in 2005, is concerned as to what the immediate future might hold, however.
Carragher, a pundit for CBS Sports, said: "The problem is not that game, forget this game, for me the big worry is that is this almost something that’s going to carry on through the season, is this the end of a cycle, have Liverpool massively got their transfer ideas wrong?
"This team looks so far off it and it has been at full pelt for five or six years under Jurgen Klopp and in seven games Liverpool have played this season, they've conceded the first goal in five, so they're not starting games well.
"I'm not going to criticise their attitude because what this team have done, certainly in Europe, the Premier League – the mentality is fantastic – but is this a massive drop off physically? Can this team get it back, that's the worry for me. What's going to happen in the future for this team?
"This is only the fourth game Liverpool have lost in 2022, it shows how consistent they've been, but the performances, more than the results, are what's worrying me right now."