The New Zealand-born coach saw his side produce some terrific results during the last campaign - especially at home.
Glasgow were unbeaten in the Celtic League at Firhill all season and recorded some fine results on their trips to Wales and Ireland.
Now the former Scotland centre wants a more even level of performance from his charges as they begin their Celtic League and European Cup campaigns.
There is added incentive to progress in the European sphere with the final set to be played at Murrayfield in May 2009
The Warriors are in Pool 5 along with last season's runners-up Toulouse, English giants Bath and Welsh side Newport Gwent.
Lineen told Glasgow's website: "Last season the Warriors narrowly missed out on a quarter-final place, so a year on there is a lot of reasons to believe that we can make a bid for next year's Murrayfield final.
"We don't fear anyone but it's about consistency. We can always raise our game for one off matches but now we're becoming consistent which is the sign of a good team but we have to keep working hard."