England's captain made the confession as his Test squad left for their timebomb tour against Pakistan.
He says he cannot be sure the imprisonment of three Pakistani players has eradicated the problem.
The decision by Pakistan to include in their Test squad three stars mentioned in the spot-fixing trial has tossed fuel on the fire.
Strauss said: "No, I don't think it's possible to say cricket is clean. There's more awareness about possible fixing but it's a hard thing to eradicate completely.
"Policing it is very tough and there's a huge responsibility on administrators and players to make sure that anything untoward is reported and acted upon. It's an odd thing to see fellow cricketers in prison but, hopefully, it sent out a very strong message that there's no place for that sort of thing in cricket."
The match-fixing row in 2010 erupted following an undercover sting by the News of the World.
The one-day series which followed the infamous Lord's Test was one of the most bitter in recent years.
But Strauss will tell his players not to get involved in personal vendettas. He added: "I don't think any good can come from churning it all up again."