The week after victory in the RDS, the Warriors fell to a home defeat against Benetton Treviso, and Lineen is anxious to avoid a repeat on a night he describes as "hugely important to our season".
The head coach told www.glasgowwarriors.org: "It's vital that we get another positive result this weekend, both to generate a bit of momentum and to reward our home crowd, who've yet to see us win a competitive game at Firhill this season.
"We were very pleased with how things went in Cardiff, but the message all week has been that we've got to avoid the same drop in accuracy and decision-making we saw between the Leinster and Treviso games.
"All the elements that combined to see us win in Wales, the powerful set-piece, the clinical edge when we created opportunities, and the relentless energy from all 23 players, will need to be there once more against the Dragons.
"We've had our ups and downs against them in the past, and we know we'll be in trouble if we allow them any chinks of light in terms of how we approach the game. We're looking for another huge, 80 minute effort from the players, with urgency and precision the key ingredients.
"If we get that, we'll stand a very good chance of giving our supporters the result they deserve after the frustration of Treviso."
Following the heroics in Cardiff, Lineen has kept changes to a minimum for Friday's match. The back division are retained en-masse, while in the forwards, Ryan Grant and Chris Fusaro come in for Gordon Reid and James Eddie respectively.
Grant and Fusaro, along with Duncan Weir, today signed two-year contract extensions that will keep them at the Warriors until at least the end of May 2014.
Lineen continued: "It's great to have those guys secured, and I'm sure they'll want to follow up the announcement with a strong performance against the Dragons.
"Gordon Reid did well on his first Glasgow start down in Wales, but Ryan is a quality performer and showed up really well in the set-piece when he came on last week.
"James Eddie also played excellently against Cardiff, and he shouldn't view this as a demotion. We're still looking to him to play a massive role on Friday, and he's exactly the sort of player you want to bring off the bench if you're looking for that bit of spark."
Glasgow have suffered defeat in just one of their last six clashes with the Dragons in all competitions, but historically the teams have been closely matched. Lineen confirmed: "It's going to be another physical battle on Friday night, and we need everyone up for the fight."
Tickets for the Dragons game are available via www.glasgowwarriors.org, by calling 0844 800 3490, in person at the Greaves Sports stores on Gordon Street and Sauchiehall Street, or at Firhill on the night. Adults £15 (£20 after 5pm on Thursday); students/senior citizens £10; under-18s £5.
Full match coverage from Glasgow Warriors v Newport Gwent Dragons will be available via www.glasgowwarriors.org, with live score updates via our Twitter feed @glasgowwarriors.
GLASGOW WARRIORS TEAM TO PLAY NEWPORT GWENT DRAGONS IN THE RABODIRECT PRO12 AT FIRHILL ON FRIDAY 7 OCTOBER (KICK-OFF 7.30PM)
15 Stuart Hogg
14 Tommy Seymour
13 Rob Dewey
12 Troy Nathan
11 Colin Shaw
10 Duncan Weir
9 Colin Gregor
1 Ryan Grant
2 Finlay Gillies
3 Mike Cusack
4 Tom Ryder
5 Rob Verbakel
6 Rob Harley (captain)
7 Chris Fusaro
8 Johnnie Beattie
SUBSTITUTES
16 Pat MacArthur
17 Gordon Reid
18 Ed Kalman
19 James Eddie
20 Ryan Wilson
21 Henry Pyrgos
22 Alex Dunbar
23 Peter Horne
ENDS
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