Ibrahimovic, 35, spurned United's best chance of the game early in the second half at Anfield, miscuing Paul Pogba's cross at the back post and directing it across the face of Loris Karius's goal.
At the opposite end, David de Gea made excellent saves to keep out long-range efforts from Philippe Coutinho and Emre Can as the hosts' five-game winning run in all competitions came to an end.
"It was difficult," Ibrahimovic was quoted as saying by United's official website about his missed chance.
"I needed to chase the ball instead of attacking the ball, but still I should have put it at least on the target. But the next game, I will do better.
"I think the game was a good game, a difficult game at the same time," the Swede added.
"I mean away against Liverpool – Liverpool are unbeaten against the top teams, seven points and I think it was a good result.
"After the second half, their chances were more, but we still worked and we can do much more, yes. But we're working hard and we're getting there."
The draw at Anfield leaves United five points adrift of Premier League leaders Manchester City at seventh, but Ibrahimovic remains optimistic that the Red Devils can mount a title challenge.
"The season is long. I see many teams are losing points at the same time. Any week, different things can happen so it is important to win the games you need to win and stay on the top," the 35-year-old said.
"I mean, if you win two games on the row you're on top. That's the way it has been so far. If we can get the wins we need to win the points then we are in touch, but it is a long season."
United have only won one of their last five league fixtures and face a testing trip to Stamford Bridge to take on Mourinho's former club Chelsea on 23 October.