Lineen has since seen stalwarts Dan Parks and Kelly Brown depart Firhill for pastures new but he maintains the Warriors can go one better this season by becoming the first Scottish side to be crowned Magners League Champions.
"I've seen a real determination in my squad this pre-season and it's about time that the Scottish teams fronted up," said Lineen.
"We have proven to be more consistent in the last couple of years and the expectations are much higher now, both on and off the field.
"Maybe in the past teams used excuses that weren't right. We can only do what we can do and there is no use in moaning and groaning about other things. That's just a waste of energy. We just focus on what we can do and what we can control. Now it's all about making the next step for us.
"It will be the hardest test but I'm hugely ambitious for Glasgow and I don't think Scotland is far from winning the Magners League. It's definitely the goal.
"With the squads both ourselves and Edinburgh have, there is no reason why we can't firstly make the top four. That would be great.
Glasgow kick-off their campaign with a home clash against finalists Leinster next Friday night.
And while some coaches may have preferred a somewhat easier start to the new season, Lineen is delighted his men will face such a stern examination so early in the year.
"We are producing a competitive team and that's why we are more consistent," added Lineen.
"For example, we picked up four away wins and two draws last year which wasn't a bad effort. I wouldn't mind us replicating that.
"We've Leinster first up but we had Munster last season and beat them. Nothing concentrates the mind like a top Irish side to get us going."
And after an historic series success for Scotland in the southern hemisphere over Argentina this summer, Lineen believes the confidence of the entire nation is growing.
"It's fair to say Scottish rugby is coming out of a dark place.
"Andy Robinson has been crucial. He's done well both locally and for the national team. He's been a huge influence for both teams. We're a tight-knit group at Glasgow but Andy comes along to sessions.
"It's a real strength for Scottish rugby and we need to keep moving in the right direction.
"But you have to be careful because you can't look back because it will bite you on the backside."
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