Missing out on victory ensured defending champions Munster leapfrogged Lineen's men into third and while Glasgow remain in the top four, they have played a game more than fifth-placed Cardiff Blues and face European champions Leinster next.
And while Lineen struggled to hide his disappointment, he is adamant the Warriors' fate is still in their own hands.
"We are still in control of our own destiny, but it makes it that little bit harder," Lineen told the Scotsman.
"This is like a loss to us because the guys are working very hard and I cannot speak hard enough of the work ethic and the culture within the group.
"Our belief is high, but we need to transfer that on to the paddock in terms of patience and maturity. The team effort is outstanding, but there are key individuals who need to learn and we will do that.
"As a team we did enough to win the game. For long periods we were down the right end of the pitch, but it was individual decisions and individual execution. We are learning at the hard end, and we will take the two points - it should have been four."
63x46.png){kind=logo}