The Liverpool boss publicly criticised the striker for his miss against Southampton.
The Reds endured a highly disappointing Sunday afternoon as they lost 3-2 to Southampton, having led the game 2-0 at half-time.
The scoreline could have been very different though as his side wasted a number of good chances to extend their lead, with Benteke arguably missing the best of the lot.
That miss saw him publicly criticised by his manager, but both Shearer and Murphy have criticised Klopp for not doing it in the dressing room.
“I understand he’s not his player and I don’t think he fancies him,” Shearer told Match of the Day 2, which was broadcast on March 20.
“But I wouldn’t take too kindly if I was a player and come onto the pitch in front of 32,000 and he let his feeling be known. Do it in the dressing room.
“Sometimes he’s great Jurgen Klopp, but sometimes he’s overly animated and it doesn’t always go down well. I agree with Alan, do it inside,” added Murphy.
Th weekend's disappointing display is just the latest in a long line for Benteke at Anfield.
The Belgian has wholeheartedly failed to impress since his move from Aston Villa in the summer as he has struggled to find a role that suits him at the club.
He has even failed to kick on under Klopp, despite the German’s outward desire to try to make things work.
This latest criticism though could be the end of that, with an exit from the club looking increasingly likely in the summer.