The 26-13 success over Bath at The Rec on Saturday was secured thanks to tries from their superb skipper Chris Robshaw and full-back Mike Brown, with fly-half Nick Evans adding 16 points with the boot in a typically assured display.
It was Quins' 11th consecutive win in all competitions, stretching back to their Amlin Challenge Cup triumph over Stade Francais in May.
But O'Shea says his side are keeping their feet on the ground, and that they will be taking things a game at a time.
"We have not set any goals," he said.
"Obviously we have goals to win matches and goals to win silverware but we don't need to come out and say that.
"We look more for a good performance and a clarity in the style we want to play.
"There are things you can't control in games, but you can control your performances."
But the former Ireland full-back readily admitted he has been pleased by a major improvement in their form away from the Stoop, which he traces back to their magnificent Amlin Challenge Cup semi-final win over Munster at the tail end of last term.
"This is our eighth straight win on the road across last season and this season so it's not bad, because we did struggle away from home," he added.
"The win in Munster, you can't say how much that meant to the players, and then how we won against Stade in the final where we hung on and won the game.
"We lost 10 games last season by less than seven points, so we knew we were a good side.
"When you come here there is going to be a contest but the confidence is there now, we have stuck to our processes home and away but what happens between the white lines is all we can look after."
Quins initially made a slow start but they gradually took a stranglehold on the key areas at the scrum, line-out and breakdown, with back-rower Robshaw and fly-half Evans once again turning in impressive performances.
And scorer Brown, believes Robshaw, who made a superb try-saving tackle on Tom Biggs early in the game, has what it takes to become England captain.
"He is a brilliant player," he said.
"He doesn't have to talk too much, he leads from the front and he shows the guys how to do it. He would be a brilliant captain."
O'Shea added: "He would be my choice (as England captain). He won the Premiership Player of the Year award a few years ago when he was just 22 and it says a lot about what other players think of him."
Bath rugby director Sir Ian McGeechan had few complaints about his side's defeat, bemoaning a costly lack of accuracy in their play.
But there is some positive news for the former Scotland and Northampton boss with the impending arrival of new signing Stephen Donald,
The All Blacks' fly-half is fresh from kicking the winning points in the World Cup final victory over France, but McGeechan says he will not look to rush the ex-Waikato man into his side ahead of their Heineken Cup campaign.
"He arrives tomorrow," confirmed McGeechan.
"We are hoping he will bring good game management, a bit like Nick Evans showed today.
"He is a clever player, you don't need to overcomplicate it, you want him to bring what he naturally has and integrate it into what we have.
"He needs an understanding of what we are trying to do and of our options.
"We will keep it straightforward and hope it accumulates over three or four games.
"We know it won't be there from week one. We will keep an open mind and see where we are. He is very excited about coming here."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.