Lineen said: "I've been really pleased with the attitude of the players and training this week has been outstanding. The players know the wins will come, we just need to keep pushing each other along and keep believing."
The Warriors enjoyed a winning start to the domestic campaign with a 22-19 victory over Leinster before slipping to an away defeat to the Dragons and home losses to Connacht and Munster.
However, the Warriors can take heart from their record against the Ulstermen. They have grabbed three wins from their last four visits to Ravenhill and Ulster's last defeat in the competition was on 16 April 2010 when the Warriors won 25-18 at Firhill.
Despite the last three results of the 2010/11 campaign, Lineen remains upbeat about the progress his team is making.
"The players have been doing a lot of good things in the games we've played so far, he continued. "It would be difficult if we couldn't pinpoint what wasn't going up to speed.
"We can't fault the players' effort at all, its just decisions and some skills at key times just not coming off.
"It's a very young forward pack. We're making errors and we're getting punished for them, and you'd expect that. But as long as we're learning, that's the key."
Looking ahead to the trip to Ravenhill, which Lineen feels is akin to Firhill, the former Scotland Grand Slam winner is expecting a ferocious battle.
"I'm expecting a really physical affair. We've had a bit of good fortune over there in the last couple of years but they've recruited well and have started the campaign well.
"Ravenhill is a great place to play, a really good atmosphere. It can be a bit like Glasgow so it's something that we're pretty used too.
"But Ulster have really stepped up in terms of their physicality and their ambition and how they're playing the game."
This fixture is live on BBC ALBA. Coverage is to be found on Sky channel 168 and Freesat channel 110. Games will also be available live on the BBC iPlayer, and archived for seven days thereafter.
Glasgow Warriors team to play Ulster in the Magners League at Ravenhill on Friday 1 October (kick-off 7.05pm)
15 Bernardo Stortoni
14 DTH van der Merwe
13 Max Evans
12 Graeme Morrison
11 Federico Aramburu
10 Duncan Weir
9 Colin Gregor
1 Jon Welsh
2 Fergus Thomson
3 Moray Low
4 Tom Ryder
5 Richie Gray
6 Robert Harley
7 John Barclay CAPTAIN
8 Richie Vernon
Substitutes: 16 Pat MacArthur, 17 Ryan Grant, 18 Ed Kalman, 19 Aly Muldowney, 20 Calum Forrester, 21 Henry Pyrgos, 22 Ruaridh Jackson, 23 Rob Dewey
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