Dundee also KO'd United from the Scottish Cup this year and boss Goodwin admits their defensive display was unacceptable as they gifted goals in a 4-2 loss that also saw Emmanuel Adeboyega red carded.
He said: "The players are hurting but we know how much this fixture means to the supporters.
"We're grateful to them for turning out the way they did in great numbers. We will take all the criticism that comes our way because it will be warranted.
"Supporters want to see passion. They want to see tackles and they want to see some aggression.
"We've had lots of pats on the back for how solid we've been. Our defensive record prior to today has been good against stiff opposition.
"But as I said, it was unacceptable and the first 45 was embarrassing at times.
"We've got a lot of looking in the mirror to do to make sure that we don't ever have a repeat performance of that in the last eight games."
Goodwin stated that the game was lost in a poor first half that lef...