Liverpool defeated United - the only team to take points off it in the league this term - 2-0 at Anfield on Monday (AEDT).
As Klopp's men moved 16 points clear at the top of the table with a game in hand, fans on Merseyside chanted: "We're going to win the league."
The win, secured with goals from Virgil van Dijk and Mohamed Salah, was quickly deemed by many significant in Liverpool's pursuit of a first top-flight championship since 1989-1990.
But Klopp was adamant he and his players still could not afford to celebrate.
"[The fans] can sing that, but they sang that a couple of times in the past, I think," he said. "There's absolutely no problem. Everybody should celebrate a situation - apart from us.
"We have no problem with that. There's nothing changed. We have exactly the same situation plus three points, which is great, wonderful, unbelievable. But nothing else has changed.
"I'll tell you immediately the moment it feels different. So far, it feels exactly the same always."
The Liverpool manager added he was looking no further ahead than their next match at Wolves.
Klopp said: "I have no idea if we can be caught or not. First and foremost, it's the Premier League. We play on Thursday against Wolves.
"They played an exceptional comeback last night [a 3-2 win at Southampton]. They have not had the results they wanted, but they've caused us here a lot of problems.
"It's the next massive challenge we face, and why should I think about more than that? I'm not smart enough to do that, to be honest. There's not enough space in my brain.
"We will prepare for Wolves, try our best, and then we will see."
Liverpool were pushed by United prior to Salah's stoppage-time clincher, with Anthony Martial missing a big chance, but Klopp claimed the visitors had set up to "annoy" his side.
"What a performance against an opponent with the quality of United and the set-up of United," he said.
"It was about, and I'm sure Ole [Gunnar Solskjaer] would say the same, [United] wanting to annoy us, disrupt our game, defend, counter-attack.
"They had moments when they played football, but it was not too often, and all the other moments were just difficult against them to create chances.
"But we did it. Wow. The manner in which we created chances was really exceptional."