The Warriors looked dangerous with ball in hand but Toulouse continually disrupted their opponents' ball at both the scrum and lineout leaving Lineen to give a typically honest assessment of his team's failings.
"At European level, you've got to get your setpiece right," said the New Zealand-born former Scotland centre.
"On our ball, they just destroyed any chance we had of getting a platform. We showed what we can do on the odd occasion that we did get the ball, but we didn't keep it for long enough.
"The scrum killed the game. We've got to get it sorted. Our scrum doesn't become bad overnight but that was a real lesson. Every time we had a scrum on our ball, or a lineout, we weren't good enough. We're better than that. We just didn't have a platform to launch anything off - I think we just had two attacks from setpiece all game.
"It's a really harsh lesson because they didn't play that well. I think they came here for the win, they got it and they were delighted with that."
Glasgow's fate was effectively sealed in the opening 40 minutes as Toulouse crossed for three well-taken tries, the third of which has to be a contender for try of the season.
And while Lineen accepts that the Toulouse attack shares few equals, he admitted he was disappointed with elements of his side's defensive display.
"Defensively, we weren't aggressive enough," added Lineen.
"They're so comfortable on the ball right across the paddock so they stretch you all over the place. Our line speed was initially quite good but they just kept the ball and they came from depth and offloaded.
"We just didn't make those first-up tackles hard enough and they managed to get the ball away. We didn't manage to stop the support runner, even though we'd practiced it all week. We gave them a channel and they took it.
"We've got to be a lot more aggressive. We just can't fall off tackles and we've all got to come up in a line. Their second try stemmed from forwards jogging up and Cedric Heymans cut past three of them.
"We gave them too many early Christmas presents and they were gift wrapped at times. One thing Toulouse like is having the ball. They're the best at it and they love it. We talked about it all week and we'll talk about it next week and hopefully have a little bit more action."
Glasgow now face the daunting prospect of traveling to Toulouse for the return fixture in a week's time, a trip that few teams enjoy as far as the end result is concerned.
But the Warriors will travel in confidence, safe in the knowledge that they are one of the small minority to have broken the mould and returned home with a shock victory over the Euro kings.
Add in the fact that the Warriors kept their tryline intact during the second half in Scotland, plus the knowledge that they scored an impressive try of their own and have a squad packed with young talent for whom fear is a word that simply doesn't exit, and suddenly things don't appear as gloomy as they might ahead of Round 4.
"We didn't disgrace ourselves but we are better than that.
"The guys did show a lot of character, there's no doubt about that. They showed a lot of spirit, they never gave up and they got stuck in but, ultimately, we needed more ball and we needed to keep it for longer.
"We scored a cracking try and I thought Richie Gray and John Barclay in the forward pack were outstanding. Max (Evans) and Graeme (Morrison) in the centre and DTH van der Merwe on the wing showed that they wanted the ball and made good inroads when they got it. But we didn't get them enough ball often enough.
"The good thing is that we've got Toulouse again next week. There's areas we need to improve but we'll go over there and go for it, why not?"