The Portugal international, who joined the Wolves earlier this month, which could cost £ 45bn, sealed the points late with an impressive strike at the Kop end.
With about 10 minutes remaining, Jota headed for the third goal before Jetta could get a hat-trick before he covered the win with his well taken strike.
Klopp was full of praise for the new man, but says he would need more time to adjust to how the Premier League champions function.
The £ 41m + deal has been agreed to take Enfield ahead of Volvo, and is set to kick for Jurgen Klopp.
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The Reds boss said: “Diogo came in, played his natural football, defending the way we do and he’s only on 20 percent of information about what we actually do.
“We had team meetings to talk about it, but it would take time.
“Today he loved 60 or 70 minutes to see how Sadio is doing and he came on the pitch and played incredibly well.
“He scored a super goal, a good first game at Anfield. So he will never forget it and I will never forget it, hence a great start.”
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Asked about a chance that Mohammad Salah got in the way of the plow before the goal, Klopp dismissed the incident as he welcomed the Egyptian international’s performance.
And Klopp was also pleased with how the entire pairing of Trent Alexander-Arnold and goalkeeper Andy Robertson went 2–1 when Sadio Mane canceled Alexander Lacazette’s opener.
“Moe didn’t get it off his leg, Moe played an extraordinary game tonight.”
“Robo, I don’t think Robo’s goal was a reaction to the situation earlier (before Arsenal) but it was just his performance and the response was really good.
“And then the goal was a cross from the right full-back and then the left full-back finished it, which is absolutely amazing, I love it.”