Klopp's side dominated throughout Tuesday's Group E contest at the Otkrytiye Arena, but settled for a second successive point to begin their campaign.
That clearly was not part of the script for the German boss, who selected an XI featuring Sadio Mane, Philippe Coutinho, Mohamed Salah and Roberto Firminho.
Coutinho grabbed his second goal in as many games, yet only after Fernando's free-kick had put the home side in front.
Liverpool subsequently spurned numerous good chances to take the spoils, much to the dismay of their boss.
He told BT Sport: "We created lots of chances and could have created more. We tried with all we have and the effort was great.
The points are shared. pic.twitter.com/BRqX9I3oJc— Liverpool FC (@LFC) September 26, 2017
"We have to be more clinical, but that's the way it is. We have to keep doing what we are doing; there were enough chances.
"It's crazy to have that many chances and not win the game."
Klopp's sentiments were echoed by skipper Henderson.
He added: "It's disappointing. We controlled from start to finish, should have won comfortably and will be disappointed going home.
"The chances we created, we have to win the game comfortably. We have got to make sure we don't give goals away
"In the worst-case scenario, it should be 1-0. On another day, it could have been three or four.
"The performance was decent but not enough to win the game. We have to finish teams off and be more ruthless."