"If you look at our form, I think we have won 12 league games out of the last 48," Simpson has told Sky Sports News.
"I have great respect for Aidy and what he has done for the club. Some wonderful things have happened with his regime.
"But the facts of the matter are that the last 12 months probably haven't been as good as we would have expected.
"I sat down with him after Saturday's game and we spoke about whether it was the right time to part company.
"We had a really sensible chat, and with great dignity and mutual respect we decided it would be best to part ways.
"It was mutual consent. We had a good chat and that's exactly what happened.
"Aidy is a good manager, he has done a lot of very good things for this club which we are very grateful for.
"But I think even young managers need a rest, and Aidy will come again. He will be a successful manager.
"It was a very hard decision but we both felt that at this point in time he had gone as far as he could with the club.
"I think it was a wonderful appointment. I think Aidy came in and he was refreshing. Look what he did."