Quins went top for the first time since the autumn of 2003 after scoring 10 tries including a 12-minute hat-trick from England number eight Nick Easter.
The battle to secure a top four spot and now sees Quins, Leicester, Bath, Gloucester and London Irish separated by just two points as the sides bid to secure a semi-final berth.
"Being top is irrelevant when we have three tough games to go," said Richards.
"We will have drawn a line under this game by 9 o'clock in the morning and everything will be geared to what is happening on Saturday.
"There is a real ambition to achieve something this year. If we are in the top four at the end of the season then I will be happy.
"We have still got to go away to Sale, Bath are Heineken Cup quarter-finalists and Newcastle are not the pushovers they were six months ago."
Bath went third with a 22-14 victory over Wasps which officially ended the Londoners' reign as champions.
Danny Cipriani's four missed kicks - 11 points that would have won them the game - put the final nail in the coffin of their hopes of a top four finish as South African World Cup winner Butch James steered Bath home with 17 points while number eight Jonny Faamatuainu added a second-half try.
But Bath have fresh concerns over captain Michael Lipman after he was taken to hospital last night with a neck injury.
The game was held up for nine minutes while England international flanker Lipman received treatment from medics and Bath were last night waiting for news on his condition.
Head coach Steve Meehan said: "The best case scenario is it is a whiplash injury. It is not concussion.
"We always treat these things seriously. When people get an injury like this, it is a concern for each and every person at this club. He has movement in his arms.
"He is a brave player, and brave players get into positions and put their teams first."
Wasps rugby director Ian McGeechan said: "We were outstanding tonight, having played the second half without the ball. I thought it was absolutely superb, probably a bigger performance than Bath expected.
"We will keep pushing on, and tonight we proved the sort of attitude we will take into every game.
"We have had ups and downs, and the players deserve more, so we will be full on until the end of the season.
"We had a bad start to the season, and that put us on the back foot. We have had to look elsewhere for the reasons why we did not put ourselves in the top at the beginning of the season."
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