Liverpool needed an 84th-minute equaliser from Mohamed Salah to escape from Old Trafford with a point, leaving them level on 71 points with leaders Arsenal after 31 games but trailing on goal difference. Holders Manchester City are third on 70.
"The whole Liverpool community just stay calm," Klopp said. "We are where we are and we keep giving it a proper go. Do I wish we had 10 points difference? Of course.
"Now people will tell us 'They have the better goal difference, we have to go for that.' That would be the dumbest thing we can do, that doesn't happen on purpose, you don't go into a game and want to score eight goals and it happens.
"We are where we are, we are how we are, and that's why we are in the race. And I'm absolutely fine with it."
Liverpool dominated the match, with United having no shots on goal in the first half while missing with a few cracks at goal themselves, including Dominik Szoboszlai's rocket that United goalkeeper Andre Onana leapt to tip over the net.
"I thought we could have scored with Dom's shot, but Andre Onana made an incredible save," Klopp said.
Skipper Bruno Fernandes scored a wild goal on United's first shot on target in the 50th minute when he latched onto Jarell Quansah's wayward pass, launching the ball into the net from the centre circle.
Klopp refused to criticize Quansah and other players who made mistakes, saying they are the same ones "who have brought us to this point."
The goal dramatically lifted the mood within Old Trafford to Liverpool's detriment, said Klopp, whose side lost a dramatic FA Cup quarter-final 4-3 in extra-time in United's inhospitable stadium last month.
"If you have that much of a dominance in a lot of parts of the game, we should win the game. Yeah, that's true," Klopp said. "But ... that doesn't mean you will win.
"I'm not over the moon about it. I don't think that's the best result I've ever seen. But I will recover."
Arsenal travel to Old Trafford to play Manchester United on May 11, and Klopp was asked if he will be rooting for United.
"Probably, if we are still around, that will be great, so probably," he said. "But Arsenal is a good football team and if they play like (their 3-0 win over Brighton on Saturday), Arsenal will win that game. I'm 100% sure. I'm really sorry to say that, but this is matter of fact.
"We should have won both games (against United) and didn't. That's our fault."
