Salah, surprisingly left out of the starting line-up, was summoned from the bench on Saturday by Klopp in the 79th minute after Michail Antonio equalised for West Ham.
The Egypt striker had a heated exchange with his manager, with fellow substitute Darwin Nunez eventually stepping in to placate his teammate.
It was an ugly end to another poor display from Liverpool, who could have at least temporarily moved level with leaders Arsenal with a victory.
They had come from a goal down, - a Jarrod Bowen header - to lead 2-1 thanks to Andy Robertson's snap-shot and a comical West Ham own goal from goalkeeper Alphonse Areola.
But Antonio's header meant two more dropped points and Klopp's final season in charge still fizzling out before the reign of the new boss Arne Slot.
Liverpool certainly did not look like a team still in with a chance of winning the title, however slim, in a first half played with all the intensity of a pre-season friendly.
With two minutes to go before halftime, the visitors were caught out by a quickly-taken corner.
Mohammed Kudus lifted the ball into the box and Bowen planted his header just out of the reach of the dive of Alisson Becker.
Liverpool hit back immediately after the restart when Diaz raided down the West Ham left and squared the ball into the area.
The onrushing Robertson took a touch before hitting a shot which squirmed between Alphonse Areola and his right-hand post.
Then came the farcical own goal which could have catapulted Liverpool back into the title race.
When Trent Alexander-Arnold swung in a corner, Gakpo prodded the ball in the general direction of the six-yard box, where all manner of chaos ensued.
Ogbonna took a swing and sliced the ball goalwards, where Tomas Soucek 's unconvincing clearance hit Areola before rolling pitifully into the net.
Areola made partial amends with a fine save from Diaz before Alisson kept out a fierce volley from Emerson Palmieri.
But in the 77th minute Bowen wriggled free down the right and lifted a cross towards Antonio, who easily got in the gap between Virgil van Dijk and Jarell Quansah as he converted a simple header.
Salah entered the fray moments later following his verbals with Klopp but had no impact as Liverpool's spluttering end to the season continued.
