United were ahead on 82 minutes through Alejandro Garnacho before Bernardo Silva found an equaliser a minute before fulltime. City then won the shootout 7-6, with Jonny Evans and Jadon Sancho failing from the spot for United.
Ten Hag later said: "Tough result to take. When the performance is right, when you lose everyone feels this. It hurts in your stomach. You have to feel pain and we have to hurt. We have to take this belief in to the league.
"We did very good to produce the second goal in the FA Cup final before half-time and weren't able to do that here.
"We managed to be on an equal level with Man City and got (Marcus) Rashford high on the pitch and good defending. We created chances, we got pressure in the ball and in possession we had some very good chances from this so there are many positives we can take.
"I think he was several times in very good positions, I am very pleased he is getting in those positions.
"Keep going and keep getting in those positions and he will score goals."
On Sancho, he added: "He is a very good penalty taker and today he missed but that is part of the game."