Jordon Ibe scored his first goal for the club, running on to Roberto Firmino's pass to slot home in the 57th minute, but Klopp was quick to assert that the 19-year-old was far from the finished product.
"He has a lot to learn, but has a really good base. Like everyone, he has to work hard... he has to learn and if he is prepared to listen, everything will be good," the German told reporters after the game.
Rubin had never lost to an English side at the Kazan Arena, claiming the scalps of Wigan Athletic, Tottenham Hotspur and Chelsea in the past, but Klopp's men dominated throughout in difficult conditions.
"The result and the first 80 minutes were really good.
"It's a really good place to play football but the pitch is not in the same shape as the rest (of the stadium).
"We did really well, we had our chances and could have had more (goals).
"It is not the biggest surprise Rubin Kazan were very well organised. I think we played much better (than in the 1-1 draw at Anfield in the first encounter between the sides)... that's normal because we've had four weeks together -- we have more experience together," he added.
Klopp travelled with a strong team, signalling his intent to take the competition seriously, unlike predecessor Brendan Rodgers.
"I only build teams or make squads to win the next game, not to give someone a rest if he doesn't need it. That's what we did today.
"We had Adam Lallana and (Philippe) Coutinho with some problems, not the biggest ones, and so they were on the bench. They could have played but we didn't risk it."
Liverpool, who are eighth in the Premier League, will hope to keep the momentum going when they host 10th-placed Crystal Palace on Sunday.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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