Quins ran in five tries in a convincing bonus-point victory to claim a third successive win of the new campaign, following successes against London Irish and Northampton.
Although he was satisfied with his side's ruthless performance in wet conditions, O'Shea sounded a note of caution and insisted the squad would not be derailed by any complacency.
"We won't be getting carried away any time because our next job is our next minute," he said. "It's not about winning the game, it's about the next minute of the next game. So we are not getting carried away at all because this is a marathon.
"We are comfortable with the way we are trying to play, the shape we have, the intensity we have.
"But we know that in the next minute of the next game, if we don't approach it with the intensity and physicality we need to, we will be blasted, and that's not going to happen.
"This is the standard we want to set. You're as good as your next game, not your last one."
With 18 players unavailable due to World Cup duty, injuries and suspension, a host of young players, including man of the match Luke Wallace, took centre stage in the Aviva Premiership clash.
Wallace grabbed two tries while Sam Smith, Ugo Monye and Chris Brooker also touched down for the Quins. O'Shea was delighted with the way the newcomers have responded to the challenge of replacing established professionals.
"The front five at the end was basically a team of kids - I thought they were pretty outstanding," he said.
"But then you see people like Jordan Turner-Hall stepping up and doing the job he did. We have to battle through this period and if the youngsters step in and put their hands up like Luke Wallace then we are in a good place."
Gloucester head coach Bryan Redpath refused to use the absence of senior players away at the World Cup as an excuse for what he termed a "rubbish" display.
"That was unacceptable," he said. "It was a poor performance and pretty embarrassing in some of it. It would be dull and rude to use players that are away as an excuse.
"I think the players were more than capable of competing and putting up a better show than that. We were extremely dull around penalties and discipline.
"We should have a good look at ourselves because that was a poor performance. We were not competitive enough.
"It's not a massive concern. If we were doing it every week I would be concerned. When you have weather conditions like that the basics have to be really good and our basics were poor.
"We turned over ball, we dropped ball and lost some set-piece. As a collective unit we were rubbish."
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