Last season's Magners League play-off semi-finalists have now gone seven games without a victory and are still searching for a win on the road.
But their woes were further compounded by a number of injuries. The Scottish side were already without 16 players due to pre-existing injuries and international call-ups.
And the Liberty Stadium loss took a heavy toll on Lineen's men with Calum Forrester, Stuart Hogg and Edward Kalman all suffering serious injuries.
"There are a lot of injuries Calum has done his knee, Stuart's done his shoulder and Edward has an ankle injury," said Lineen.
"There's a lot of sore bodies across the board.
"There was a lot of confidence and leaders already missing. We were without 16 players, 13 of those starters, and overall ability in certain areas just isn't there.
"It was very physical, we knew what the Ospreys would bring and they punished us on turnovers.
"In defence we had no line speed, there were high tackles and we made it easy for them."
Despite what the scoreline suggests, the game was anything but one-sided and Glasgow had plenty of opportunities. But Lineen's unexperienced side lacked composure and were unable to turn pressure into points.
"Six of the backs were under 21 and when you don't have a platform to work off it's very tough," said Lineen.
"There were good things and the boys are trying, but the scrum got smashed and there was no platform.
"It doesn't help that we butchered two tries in the first half. It's just a composure thing.
"On the left Peter Horne just needed to give the ball to DTH earlier. When he got the ball it was too late.
"On the left Peter Horne just needed to give the ball to DTH earlier. When he got the ball it was too late.
"But Peter's a young guy who wanted to score but took the wrong decision. Then Peter Murchie made a similar mistake on the right.
"The good thing is we are making these opportunities and the spirit is there. These guys are learning but they are learning the hard way. We have to dig in to get through this patch."