The DRS has been a constant source of controversy during the current Ashes series, with the Hot Spot technology in particular coming under scrutiny after several failures to record fine edges.
Richardson told BBC Radio Five Live's Sportsweek programme: "What we need to do now is take stock, review the statistics.
"I think maybe there's an appetite for a debate about not only the detail of the process and the way technology is used - the number of reviews or whether it should be the umpires making the request or the players - but some philosophical debates now as to DRS; are we allowing enough benefit of the doubt to the batsmen?
"The time is right to maybe take a backward step but not to forget the statisitics.
"Just looking back over the five Tests, we again see that without DRS we would have had a correct decision percentage of about 91 per cent, which is lower than we like and lower than the average.
"With the DRS, we've ended up with the correct decisions about 97 (per cent), so again an improvement of around five or six percentage points."
There is a possibility that come the return Ashes series Down Under this winter, umpires could have access to the Snickometer technology already used by television broadcasters.
Richardson said: "One of the things we need to look at is other technologies to improve that situation, to provide conclusive answers on more occasions.
"The good thing about Hot Spot is that when there is a mark, then we know there is an edge.
"Sometimes it doesn't pick up the faint edges and we know that. It's going to help us get to 97 per cent but not to 100 per cent at the moment.
"They're looking at a technology called real-time Snicko which, perhaps used with Hot Spot, will make determining edges much easier.
"That'll probably be the first little piece of technology that's more likely to be introduced than any other. It's always been very reliable.
"The one that's been trialled in this series, the real-time Snicko, it's available quickly. It is a visual depiction of the sound from the stump microphone so it's quite an involved process making sure that the sound is synchronised perfectly with where the ball is. It's not as simple as people might imagine.
"There are Chief Executives' Committee meetings coming up in December, and they could have the authority to sanction its use. We wouldn't do that, though, until we're satisfied 100 per cent that they've got that whole process of synchronising the sound with the vision perfect."
Regardless of what technology is eventually introduced, though, Richardson does not believe the sport will ever achieve 100 per cent accuracy in umpiring decisions.
"I don't think it will be achievable," he said. "Technology will fail from time to time and umpires, even with technology, might make a mistake as far as judgement is concerned.
"With human beings involved in implementing the technology, they will make mistakes.
"I don't think we will get 100 per cent, I don't think we should necessarily be aiming for 100 per cent."