But they made a huge statement against top-four rivals Munster, as Glenn Bryce's late try secured a bonus-point victory in Kilmarnock.
Glasgow are still 11 points behind fourth-place Ulster but have two games in hand after postponements earlier in the season.
Their next challenge is at Newport Gwent Dragons on Thursday - and back-rower Strauss admits the points took far greater precedence than the performance on this occasion.
"It's massively important, after last week we said that's it, we've got to turn the season around, and statistically we had (to beat Munster)," he said.
"Great character was shown, we're obviously happy but not completely as we made mistakes - myself included.
"We've got a short turnaround before Thursday and we have to play the whole 80. Especially on this surface we wanted to play our fast game and get our backs involved.
"But if you do one thing right you can't let another thing slip and our defence wasn't good enough - and it's something we pride ourselves on."
Strauss has only appeared seven times in the GUINNESS PRO12 this season after a spell on the sidelines, but the 29-year-old put in 14 tackles and made 104 metres in an all-action display.
"I just wanted to focus on my game," he added. "It's been a bumpy season for me, up and down with injuries and time off, I just wanted to get myself back in it.
"It wasn't 100 per cent, there are things I could have done better and things I did well. You always strive for excellence - you want to do better."
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