But Lawn told BBC Radio Leeds: "They have let Peter Taylor down - without any doubt at all.
"They haven't performed have they? If they had performed as a unit we wouldn't be where we are."
Taylor had earlier stated that he decided to leave Valley Parade after the fans' reaction to their mid-week defeat to league leaders Chesterfield.
It means Lawn and joint-chairman Julian Rhodes will be holding interviews for a new manager for the second time in just over a year.
"We will start interviewing next week and will see then who is interested in the job and who is not," he said.
The players have to take a long, hard look at themselves because they have let Peter Taylor down
"Sometimes I think there is a curse on this club because I defy anyone to turn around and say Peter Taylor was not the right man for the job.
"He had an impeccable pedigree but it has just not worked for us. Let's pull no punches, it just hasn't worked.
"Whoever we get in now we need to ensure he has a squad that can perform in front of 10,000 fans and not 3,000.
"They have to be able to perform and feel comfortable in front of 10,000 because that's not been the case with the players this season. They have to take a long, hard look at themselves because they have let Peter Taylor down.
"I will be looking for them to give a response on Saturday to ensure Peter Taylor goes with a win. I think that's the least they deserve to give him. "
Source: BBC Sport