And with the 1872 Cup now on the line when the two Scottish RaboDirect PRO12 sides meet over Christmas and New Year, Lineen believes both sides are well-set for a successful season.
He said: "[The draw] keeps us in the hunt - just," said Lineen. "It's great that Edinburgh had a result against Cardiff - it's good that the Scottish teams are doing well.
"There's huge progress and we're getting good support. The players enjoy it - but, ultimately, it's about getting wins and points.
"We'll take the two points, but it could have been four."
Glasgow made a slow start in the south of France with Montpellier winger Yoan Audrin scoring the only try of the first half.
And despite fighting back thanks to a powerful scrum and the boot of replacement Duncan Weir, they were grateful for Paillaugue's late miss to save them from defeat.
Lineen added: "Obviously, in the first half, we didn't do ourselves any favours.
"We played a bit too deep and made some basic errors that we usually wouldn't.
"That comes with the pressure of European rugby, but they'll learn from that.
"Simple things needed to be done better. Our scrum was good, subs came on and made a huge difference.
"But you can't defend in the first half for 30 minutes and expect to win the game.
"We'll have to look at that again - the first half just wasn't good enough."
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