Howe was wanted by both Palace and Charlton, but, after he opted to stay with Bournemouth, Parish turned to legendary ex-Palace striker and caretaker boss Freedman for the permanent manager's role.
"It's no secret we were interested in Eddie - I'm not going to suddenly pretend we didn't want him," Parish told the South London Press.
"He is very much in the same vein as Dougie but has got a couple of years' more experience, we looked on that favourably and it maybe just tipped the balance.
"We talked to Eddie and we liked him - I think he's a fantastic guy - and his assistant but they decided to stay at Bournemouth and I'm genuinely pleased for them and their fans. I wish them all the best.
"Now I want to concentrate on Palace. We've got somebody very much in the same vein. Dougie hasn't got a couple of years' experience but he has a bit more knowledge of the Championship."