Sampson was cleared of racism, harassment and bullying allegations made by Chelsea player Eni Aluko on two separate occasions and, according to the Football Association, his dismissal is not linked to said allegations.
"I won't lie, it's been a very testing time, probably one of the most difficult things I've dealt with in my career," Hayes told Sky Sports News after Chelsea beat Bristol 6-0 in their first Women's Super League match on Sunday.
"I think it's a tragic ending to what has been a very difficult time for everyone involved including the FA. I hope moving forward that the combination of the select committee and the FA reflect on the whole handling of the situation and going forwards they make sure it never happens again.
"It's been a very tricky case, where there's been an awful lot involved and revealed at different times and because of that, I think that it's best it's left with the select committee for them to make decisions where the FA need to improve, because it's very clear that they need to."
Sampson has led the Lionesses to two successive semi-finals in major competitions in the past four years.