Ten Hag said, "It was an incredible game, a strange game too. We had total control for so long and then gave it away in the last part of the game. We did show resilience to win the penalty shootout.
"We had control for 75 minutes and have to give Coventry a compliment for what they did in the last 15 minutes.
"We have to improve. We talk a lot about this. First you have to put yourself in a winning position but then you have to take it over the line. In these moments we are making mistakes and not keeping our responsibilities.
"We can't say this group doesn't have the right mentality because they showed character today, but in the final part there was a lack of discipline.
"We have to keep the ball, keep making passes, go for goal and then also be strong in defence. It's about communication and we have to improve on this."
On what he said before penalties, he said: "It was about mentality in that moment. You have a plan and have full confidence so I told them to stick to the plan.
"I had confidence we would win the shootout. Normally Casemiro scores, we train them very well."
On the feeling in the group after the game: "It's mixed feelings. We can be happy with the achievement, getting to the final, that's huge.
"Even the big Manchester United only achieved it three times and we achieved it twice in two years. We need to win that final though. When we 100% in it then we can do it.
On whether they need to win the FA Cup for it to be a successful season, Ten Hag added: "I want to win it. I'm sure we have a good chance to win this final, although we play the best team in the world.
"We do have a chance though. We showed that this season.
"This season has had many ups but also many downs. Winning the FA Cup doesn't make it successful, we want to win more.
"We have been in three finals in two years, which is good, but we had a lot of setbacks this season.
"We've had a lot of injuries and hopefully those players can be back for the final. If we go with a squad who believe then we have a chance to win a trophy."