The visitors took the lead in the 15th minute through Marko Devic’s half-volley but had captain Oleg Kuzmin sent off for a second booking shortly after.
Liverpool responded and drew level when Emre Can stabbed in following a free-kick in the 37th minute.
The Reds dominated proceedings in the second half but failed to make the man advantage count and were forced to settle for their second successive draw under their new manager.
The game prompted plenty of activity on Twitter – and here are some of our favourite updates.
— Ian Rush MBE (@Ian_Rush9) October 22, 2015
— Rob Jones (@RobjonesLFC2) October 22, 2015
Supporting my two teams for tonight… Ajax & LFC!!! Good Luck…
— Ryan Babel (@Ryanbabel) October 22, 2015
— BT Sport Football (@btsportfootball) October 22, 2015
Hahahaha yeeees. Love to hear the song from home… #ynwa
— Luis Garcia (@LuchoGarcia14) October 22, 2015
Don't think you can judge Klopp on this Europa League performance,personally I can't stand the competition
— mick quinn (@mickquinn1089) October 22, 2015
You can't make chicken salad out of chicken shit ……
— Rodney Marsh (@RodneyMarsh10) October 22, 2015
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