Freiburg, who are fourth in the table and had lost their previous three games, went 2-0 up inside five minutes and became the first team to score five times away from home inside the first 25 minutes in a Bundesliga game before adding a sixth in the 37th minute.
Monchengladbach also lost their previous game 4-1 to FC Cologne and are now 13th on the standings.
"I am incredibly disappointed," Hutter told the official club website. "I'm also very sorry for the spectators who made their way to the stadium. We win together and we lose together.
"A few weeks ago, we beat Bayern 5-0 here and we were all over the moon. Today, we saw a match that should never have played out the way it did. Of course, we knew that Freiburg are strong from set-pieces and we prepared for that in training, but I had the feeling that we were paralysed from them.
"I don't have an explanation for that right now. First and foremost, we have to apologise for the way we played today. That is unacceptable. If you saw the level in training, you would never imagine that a performance like that could happen. But then when you're 5-0 down after 25 minutes, it's obviously very disconcerting."
Sporting directer Max Eberl added: "We conceded two early goals, and you could see how nervy it made everyone. No one wanted the ball, although, to be honest, we didn't have much of the ball in the opening period anyway.
"We just had this inexplicable lethargy and didn't carry a threat at all. I'm a bit bewildered right now. Tomorrow is about picking ourselves back up and digesting the defeat. We conceded four goals in Cologne, and now six today, but we also didn't do enough going forward with enough incisiveness either."
Monchengladbach are away to RB Leipzig in their next game on Saturday.
