Salah's number was shown in the 64th minute at the Amex Stadium on Saturday, with the Reds leading Brighton by a goal to nil.
And the Egyptian was far from impressed at having to make way for Sadio Mane.
BT Sport cameras showed Salah uttering something under his breath as he made his way to the touchline, where Klopp moved towards him.
The Reds forward then briskly walked past his boss, without making eye contact, prompting Klopp to pat him on the back.
Klopp insisted: "The day when Mo Salah is smiling when he leaves the pitch something is really wrong.
"So I get it, 100 per cent.
"The problem is he had COVID, was out for 10-12 days, trained once, played 60 minutes, three days later, played again.
"We just have to be careful, he doesn't like it I know but that's it."