He was offered a coaching job at the County Ground, but rejected it, so will now leave the club.
Onoura said: "I have spoken with the Board and they have mapped out their plans for next season. It has happened fairly quickly but whilst I am disappointed, I understand that the club want that big name to put bums on seats early in the season, which is important.
"There was an offer to keep me at the club, but in reality the new manager will want to look at the club from the bottom up and he wouldn't want the former manager sitting in the wings. I don't think that would have been beneficial and I guess there would have been a little bit of pride at stake too, I'm not afraid to say that.
"The circumstances were unfortunate. I look back on the chances missed, posts hit and penalties not converted, but that's just how narrow the margins are in football. The reality is that if we had stayed up, the whole thing would have been looked at differently
"I don't harbor any grudges and will look back at my time here with a lot of fondness. The fans have been magnificent from day one and I will dust myself down and get on with things."