But the panic button has not been hit according to Josh Strauss who produced a man-of-the-match performance in the Warriors' 24-15 defeat at Franklin's Gardens.
Playing in what was only his third match, and his second start, for the club since he signed from the Johannesburg-based Lions last month, Josh put in an all-action display and scored the first of Glasgow's two tries as they built up a 15-0 lead inside the opening half-hour.
However, disrupted by injuries, Glasgow's advantage evaporated over the next 20 minutes, although Josh believes the team can regroup and still make an impact in the European competition.
"Obviously, you want to start well," said Josh. "But if you lose one game you don't want to go into panic stations and try to change things. There were a lot of positives to take out of the game, especially the first 35 minutes, which were exceptional.
"At the end of the game, the guys showed a lot of character in defence, keeping Northampton out when they were in our territory so much. Obviously there are a lot of things we can work on, but we can also take the positives and build on them too. I think we should do really well this season."
Ulster made the perfect start to their Heineken Cup campaign with a bonus point as they beat Castres Olympique 41-17 at Ravenhill.
Springbok scrum half Ruan Pienaar was among the scorers for Ulster, and Josh is relishing the prospect of facing a side which has had a considerable South African influence in other areas in recent seasons.
"Watching the Heineken Cup from South Africa, Ulster were one of the teams to be reckoned with," said Josh. "I've seen the South Africa flags being waved at their home games and I'm really looking forward to playing them."
Ruaridh Jackson and Stuart Hogg went off with injuries at Franklin's Gardens but are hopeful of making Friday's match although the news isn't so good for Sean Lamont, who looks set to miss out.