The centre-back headed home after goalkeeper Simon Mignolet had parried Richarlison's shot against the woodwork as Marco Silva's side snatched a point in a dramatic 3-3 draw at Vicarage Road.
Britos was standing behind the last Liverpool defender when Richarlison struck his effort, but the referee's assistant chose not to raise his flag, allowing the goal to stand.
Watford had taken the lead through Stefano Okaka's header from an early corner and restored their advantage through Abdoulaye Doucoure after Sadio Mane's equaliser, before Roberto Firmino's penalty and a goal from debutant Mohamed Salah put Liverpool ahead.
Liverpool's defence were criticised for conceding from three crosses after the match, but Klopp insisted his side's failure to see out the win was the fault of the officials.
"It was an away game as the first game against a physically really strong side," he told Sky Sports. "We started with not enough direction but did much better in the second half.
"We came here to win and I think that would have been deserved. Watford had their moments but pretty much around set-pieces. The first was good, the second unlucky but the third goal was offside.
"I was not too happy with the positioning when we were 3-2 [up], we were a little bit too deep and it means the long balls in behind, if you lose it, it's directly a chance.
"The first was a really good cross, it's not a team problem. The second was really unlucky because we'd already defended it, but again it's formation. I think Alberto [Moreno] loses a really high challenge and there should be another player, then you can't play the pass in behind.
"But if you concede offside goals, you can't defend them.
"We knew that before, of course, but after this game, we have a lot of things to do. If we win 3-2, we have a lot of things to do, now it's 3-3 and we have a lot of things to do. But we also showed a lot of good situations."
Salah won the penalty from which Firmino scored before bundling home from close range to cap a strong first competitive performance following his club-record transfer from Roma.
Klopp felt he took time to get into the game in the first half, but was pleased with the Egypt international's overall contribution.
"Good, he struggled a little at the beginning, playing too much on the wing," he said. "It's difficult to play on the right-hand side, [Jose] Holebas is a real strong boy. He's also really quick.
"Then we started working direct and we were immediately unbelievable, difficult to defend. Overall, it was a good performance."