The Reds suffered a surprised 4-0 defeat to Erik ten Hag's side in Bangkok on July 12, but they fielded three separate teams against a strong Red Devils line-up.
The 23-year-old joined Liverpool in a club-record £85million deal from Benfica in June.
He had an unofficial debut to forget after spurning a golden opportunity to net his first goal for the Reds, blazing over from close range at the Rajamangala National Stadium in Thailand with plenty of goal to aim for, after Mohamed Salah's effort came back off the post.
It did not take long for his miss to go viral on social media, while footage of him missing chances in training sessions have also done the rounds. But Klopp was quick to dismiss the jibes aimed at his new marksman.
"I'm not worried at all," the Reds boss told reporters when asked if there was potentially a need to preach caution with a player coming with such lofty expectations.
"The general judgement [on Nunez] is absolutely nil interest [to us]. It will be like this, and we all know it.
"It's kind of a game or a joke for some people to pick out some situations where a player's not doing well. That's only a game from [fans of] other clubs, which is normal.
"Our fans probably do [the same] with signings of Manchester United. We cannot take this seriously."
Klopp has since told the club's supporters to get behind their new striker and forget his sizeable price tag.
"The only real important thing is how I judge the situation for the player and I couldn't be more calm, I'm completely convinced about his potential," Klopp added.
"And actually, what our people, all Liverpool supporters in the whole world, should know is that new players need time and get time.
"We should be the first ones to delete the fee we paid [from our thinking]. Just delete it, it's not important.
"It's like this with strikers. He missed a chance and then there are some nervous people going, 'oh my god, he missed a chance', I can promise you it will not be the last."
Nunez, who netted 26 goals in 28 Primeira Liga appearances for Benfica last season, will be hoping to get off the mark when Liverpool taking on Crystal Palace in their second pre-season clash in Singapore on Friday.