Ole Gunnar Solskjaer refused to celebrate a hard-earned point at Anfield, pointing out that Manchester United are now required to win their next outing to keep up their Premier League chase.
Liverpool were held 0-0 by the leaders on Sunday, a result that meant Jurgen Klopp's men missed out on the chance to retake the summit from their arch-rivals.
United lead by two points over Leicester City with 18 games played, with the Merseysiders a further point back in third.
Aside from a late flurry of chances the Red Devils had few opportunities to win Sunday's title six-pointer, and Solskjaer warned that his charges cannot rest on their laurels with another Premier League test away to Fulham looming on Wednesday.
"It's only a good result if we win the next game," the manager explained to BBC Sport after the final whistle.
"It was an opportunity missed with the chances we had but then again we were playing a very good side. I'm disappointed but still a point is OK if you win the next one.
"We were stronger towards the end. We didn't start at all in the first half. We didn't have any composure or try to impose ourselves.
"The team is working hard for each other. We have improved and progressed. It's not just the result we're disappointed with, it's some of the performance. I know these boys can play better.
"Fair play to them - with two central midfielders at the back (Fabinho and Jordan Henderson) and to defend as well as they did shows their quality."
Solskjaer added to Sky Sports : "I think we grew in the game and toward the end it was there for us to win. We created two massive chances and it was two brilliant saves by the keeper.
"We can play better than this, we can be more composed, we can have the ball more. We had to defend really often today. There are a couple of things for us to improve on
"I thought Paul [Pogba] was absolutely brilliant today. We knew he had to do a job defensively to help us with [Andy] Robertson and I thought he was excellent and should have got the goal his performance deserved."
