The win was sealed by Federico Aramburu's 76th-minute try, with Duncan Weir kicking four penalties and Ruaridh Jackson one as the Warriors maintained their pursuit of European champions Leinster in the standings.
Lineen rated his side's second Heineken Cup success from three games a C+ and knows a vast improvement will be required in southern France.
Lineen said: "We've got to go with a realistic ambition of winning the away game. It's going to be incredibly tough.
"If we play like we did in the first half today, we'll be 30 points down.
"We need to make sure we go across there, get the basics right.
"They've got some fantastic players and when they get their momentum going they're incredibly difficult to beat."
Montpellier's tries came through Eric Escande and substitute Masi Matadigo - a late score which secured a losing bonus point - with Martin Bustos Moyano adding five points from his boot.
"Unfortunately, giving them the bonus point takes the gloss off a bit," Lineen added.
"We needed to tighten up there. We got a bit carried away trying to score, going from two metres from their line to them scoring at the other end shows what they're capable of."
Montpellier were without some of their stars and captain Fulgence Ouedraogo, Georgian powerhouse Mamuka Gorgodze and inspirational fly-half Francois Trinh-Duc are likely to be back for the return.
Nonetheless, Lineen was thrilled with the result which puts the Warriors three points behind Leinster with three matches remaining.
Lineen described the first half as "a little bit scratchy".
He added: "The players just needed to go up a couple of gears - we're just getting these wins.
"If we had kept the tempo, kept the ball a bit longer in the right areas, we could've perhaps scored a couple more tries.
"But this is a fantastic win. To cap it off with a great set-piece try was absolutely marvellous."
Lineen praised the performances of Chris Cusiter, Stuart Hogg, Richie Gray and Jackson and was pleased with Rory Lamont's contribution on his second Warriors debut after re-signing from Toulon, despite the Scotland back being a peripheral figure in the first half.
"We've got Rory in and it was as if they didn't want to give him the ball in the first half," Lineen said.
"He got through that first tackle and kept the ball alive really well.
"He's buzzed up. I had a chat to him after the game and he loved it - he loved the 40 minutes he played and we just need to look at how we get our big ball carriers involved."
Lamont was signed as a full-back, but 19-year-old Hogg held that jersey today and excelled, laying on the try for Aramburu.
Lineen said: "He's played brilliantly all season. He's a top lad and he's got all the skills and he backs it up with making good decisions and having a go."
Scotland head coach Andy Robinson was present at Firhill and will surely be considering calling on Hogg for the RBS 6 Nations.
Man of the match Hogg, though, is prepared to be patient.
He said: "It's a dream to play in a Scotland jersey, so hopefully one day it will come.
"Right now I'm just happy to be in the Glasgow team and I'm really working hard on my game. I've still got plenty of time."