The final episode of the current series drew an average audience of 7.5 million on Tuesday.
The BBC has yet to confirm if the Yorkshire-based show will return, but Wainwright she wanted "time to go away and really come up with stories".
She would hate to make a series which "people say wasn't as good", she added.
Wainwright, who created the series, told BBC Breakfast she was "so busy with other projects at the moment, I haven't got time to sit down and come up with stories", agreeing there "might be a wait" for a third series.
The drama, which stars Sarah Lancashire and James Norton, has been praised by critics, with the first series winning best drama at the Bafta awards in 2015.
However, the second series has received criticism for poor sound quality and mumbling, a problem which Wainwright said had "mystified" the production team.
"When it leaves the [editing suite], the episode is perfect - it has to be," she said.
Wainwright - who has also worked on the BBC's Last Tango In Halifax and ITV's Scott & Bailey - added that producers listened to the episodes on regular televisions before transmission to ensure the sound was clear.
"As the series went on, we became more conscious of listening really carefully... we all brought a very ordinary telly in to listen to it on that," she said.
"I do find it bemusing that for every person that said 'I can't hear it', there were as many people saying 'I can hear it'," she added.
Screenwriter Sally Wainwright has said she is keen to write a third series of BBC One drama Happy Valley, but wants enough time to think of new plotlines.