Result we will have to accept
The home side headed into this crucial clash, bang in-form with nine consecutive victories and remaining 15 games unbeaten.
However it looked like that run was going to come to an end against Jurgen Klopp's side, with James Milner slotting home a first-half penalty.
United managed to secure a point with Zlatan Ibrahimovic's late effort, but Mourinho stated that he was unhappy with the full-time result.
"The result is not the result we wanted," Mourinho told manutd.com: "It’s not the result we fought for." He stated, "But it is a result we have to accep. It was a very emotional game."
Mourinho added, "I believe both sets of players are very tired because they gave everything." The United boss commented on the two teams also, "But I think Manchester United can play better than we did. I also think Liverpool can play better."
He continued, "So the game was below the quality of both teams but in terms of a proper Premier League match and a derby, it had a lot for people to enjoy."
Had to be Marouane
Mourinho made a defensive decision in the closing stages, with Marouane Fellaini coming on instead of the forward thinking Marcus Rashford.
The decision was made to help the balance the side as they looked for the eventual equaliser and a possible winner, and Mourinho stated the Belgian's importance to the side: "I had one more option: Fellaini or Rashford but I saw so many yellow shirts in the box, in front of the box."
The Portuguese explained, "I thought probably my players would lose a bit of the emotional balance, and would go for a more direct approach."
Mourinho concluded, "To go with a more direct approach it has to be with Marouane, he was an important player for us."
Manchester United will visit Stoke City at the Bet365 Stadium on Saturday, January 21 with kick-off at 3pm GMT.