But coming off the back of a rousing 22-19 victory over Leinster last weekend, Lineen has every confidence that the Warriors can continue their impressive form when they visit Rodney Parade.
"This is a huge game," he said. "We had a good away record last season of four wins and two draws, but we're travelling down to Newport and it's going to be difficult.
"All six home teams won at the weekend so it's going to form in terms of home advantage but it's going to crack at some point and it would be great for us to do it against Newport on Sunday.
"Newport are going to be tough but it's a good one to get after the high against Leinster."
On the importance of starting the season with a win in front of the home support at Firhill, Lineen continued: "It was really important to get a win first up at home in front of the crowd. The new guys all did well and the subs were fantastic when they came on. It was great to see the smile on the players' faces after the game.
"But it's a long season and it's my job to make sure we're organised, prepared and motivated for the game ahead."
The Warriors have made two changes to the starting XV that defeated Leinster last weekend, both of which are in the forwards.
Ed Kalman starts at tighthead prop in place of Moray Low who is named among the replacements whilst Canadian international Chauncey O'Toole, who joined the Warriors on a short-term contract this week, is named at blindside flanker in place of Ryan Wilson who drops out of the match-day 23.
The most notable inclusion on the bench is that of utility back Colin Gregor who is poised to make his return to frontline action following knee surgery at the end of last season.
The game will be broadcast live on BBC ALBA. Coverage is to be found on Sky 168 and Freesat 110. The game will also be available live on the BBC iPlayer, and archived for seven days thereafter.
Glasgow Warriors team to play Newport Gwent Dragons in the Magners League at Rodney Parade on Sunday 12 September (kick-off 4.10pm)
15 Bernardo Stortoni CAPTAIN
14 DTH van der Merwe
13 Max Evans
12 Graeme Morrison
11 Federico Aramburu
10 Ruaridh Jackson
9 Henry Pyrgos
1 Jon Welsh
2 Fergus Thomson
3 Ed Kalman
4 Tom Ryder
5 Richie Gray
6 Chauncey O'Toole
7 Calum Forrester
8 Richie Vernon
Substitutes
16 Pat MacArthur
17 Moray Low
18 Ryan Grant
19 Aly Muldowney
20 Rob Harley/Chris Fusaro
21 Colin Gregor
22 Duncan Weir
23 Hefin O'Hare
63x46.png){kind=logo}