Salah is comforted by team-mates and opponents alike after injury forces him off in the final. ─ AFP
The Egyptian hurt his left shoulder as he went down in a challenge with Sergio Ramos in the 25th minute.
Five minutes later he made way for Adam Lallana, and his presence at the World Cup is now in doubt.
"We wanted everything and got nothing. We lost an important player and probably Egypt lost for the World Cup an important player," Klopp said.
Salah's injury, and that which forced Real's Dani Carvajal off before the break, temporarily took the sting out of the game after an enthralling start, with Liverpool on top.
After Salah departed, Real sensed their chance. They even had the ball in the net in the 43rd minute, only to be denied by a marginal offside call.
Ronaldo's header from Isco's cross was parried by Karius, and Benzema turned in the loose ball, but the flag cut short his celebrations.
If that was a let-off for Liverpool, they were their own worst enemies at the start of the second half.
Careless Karius
Isco struck the bar after Lallana diverted the ball into his path, before Benzema opened the scoring in the 51st minute.
It was a moment of unbelievable carelessness from Karius, who attempted to roll the ball out to the nearest red shirt only for Benzema to stick out a leg and send it trickling into the net.
Klopp's side really could have let their heads drop, and yet they were soon back level, Mane turning the ball in after Dejan Lovren headed down James Milner's corner.
But their renewed hope was crushed upon the introduction of Bale.
The Welshman had been on the field barely two minutes when he met Marcelo's cross from the left with an improbable leap, back to goal, 15 yards out, to send an overhead kick on his left foot arcing over Karius and in.
Such a strike deserved to be the winner, although it was his long-range shot that beat the embarrassed Karius in the 83rd minute that made sure of the victory.
Mane hit the post for Liverpool in between Bale's strikes, but they will have to wait a while yet before winning their sixth European Cup.