The right-back will leave Town when his deal expires at the end of June and claims that the club reneged on a verbal offer of an additional one-month deal which would have seen him remain there for the rest of the season.
Terriers chief Danny Cowley admitted to being frustrated that a deal could not be agreed to ensure that the ex-Leicester City full-back would stay put.
Simpson tweeted: “Unfortunately, finishing the season the way I planned wasn’t meant to be, so I feel it’s only fair that I am honest and I explain to the fans that treated me so well.
“Last week, me and the club had verbally agreed a one-month extension which the club withdrew one hour and a half before kick off against Wigan.
“I am saddened by the outcome and the way the situation was handled.
“To leave the club in this manner is disappointing, but I believe the boys and the manager will fight and achieve the aim of staying in the Championship next season.”
On Simpson’s exit, Cowley said: “It was not possible and we have to accept and understand that. While it was disappointing for us and the club and also for Danny, we have to move forward. This is what you always have to do in life and football.
“Danny wanted to stay, there’s no doubt about that and we wanted Danny to stay. But we couldn’t make it happen and that was frustrating, no doubt about that. But this happens in football.
“In regards to Danny, he did great for us.”
Meanwhile, Cowley has stressed he will not jeopardise the future fitness of strikers Steve Mounie and Fraizer Campbell and insists they will only feature in Sunday’s Championship game at Nottingham Forest if he is confident about their condition
The pair missed last weekend’s defeat to Wigan due to a quad problem and a slight Achilles issue respectively and the Town chief is mindful of jeopardising their involvement in a crammed schedule in July if they feature at the City Ground when they are not quite right.
He said: “We are hopeful that they will be back and we will be able to use them.
“(But) We know we have eight games coming very quickly and we cannot afford to make mistakes in terms of bringing them back too soon, as we know that could be fatal for their season.”
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