The hosts enjoyed over 70 percent of the possession but could not create clear cut chances with Nick Pope untested for larger parts of the game.
Chris Wood got the opener for Sean Dyche’s men on the cusp of halftime before former Southampton forward Jay Rodriguez sealed the victory 11 minutes into the second half.
After seeing his team lose for the eighth time in the Premier League this season, Solskjaer said the Red Devils must be gutted following such a terrible performance.
"We have got to hold our hands up and say it wasn't good enough,” the Norwegian coach told reporters.
"In the first half we created some half openings but we were not sharp enough to take our chances. They were clinical and efficient and defended well. We couldn't open them up.”
"The boys have given everything they have got but they are experiencing this period for the first time in their lives.”
“When you are at Manchester United you are playing at the biggest and best club in the world. Some of them have played 10, 12, 15 games and it's not easy for them.”
"I'm going to back them and help them get through this. We can't do anything but hold our hands up and say it's not good enough.”
"You can talk about it all day long and we are disappointed with our points tally. We work every single day for these boys to improve and perform better than this."