Last year's Champions League and English Premier League runners-up have had a faltering start to the season, losing their opening game in Europe to Napoli and sitting a relatively lowly ninth in the domestic competition.
But they brushed aside their Scottish opponents at Anfield with a 2-0 victory that would have been a bigger margin had it not been for Rangers goalkeeper Allan McGregor's heroics.
"I liked the game a lot. We got three points. That's the important thing," Klopp said, looking happy but more subdued than usual after a European win that left Liverpool second in Group A on six points after three games.
"I can't wait for the moment when I can read newspapers again. But the criticism is completely fine. We are not over the moon about our situation," he said of the reaction to Liverpool's latest leaky performance in a 3-3 draw at home to Brighton at the weekend.
"I saw tonight a team fully committed, that's what I like a lot. It was exactly what we needed tonight. A new formation, we had to change things. We had plenty of chances, imagine if we had taken more of them. Really good game. Very important.
"We expected a reaction. Everyone expected a reaction. We really want to turn this into a positive and for that we need consistency. For that, you need top-class defending and we had that tonight. It worked out pretty well."
'WONDERFUL GOAL'
Right back Trent Alexander-Arnold has been particularly under fire of late for Liverpool, criticised for leaving gaps in defence as he marauds forward.
Yet he got it all right on Tuesday, scoring a spectacular free kick to set Liverpool on the path to victory while also helping to keep a clean sheet.
"He played a good game, defensively especially. And a wonderful goal, eh? I am happy that he had that," said Klopp, noting some tweaks in the formation to give Alexander-Arnold more cover when he went forward.
"We take risks. We were not in the perfect moment, that's why we adjusted it."
Klopp, whose team are three points behind Napoli in Group A though still in a qualifying position, said he expected a very different game when Liverpool face Rangers in Scotland next week. "We respect them a lot," he said.
He was delighted with his front four of Mohamed Salah, Darwin Nunez, Luis Diaz and Diogo Jota.
"The way the boys moved up front today was extremely good," he said, saying Nunez was bound to score soon after a string of saved shots against the Scots.
"Two set piece goals as well - I love this as it means you don't need to wait for VAR!" he quipped of Alexander-Arnold's free kick and Salah's penalty.
