The striker was released from his contract on the eve of last weekend’s 3-1 victory over Grantham Town at the Sir Tom Finney Stadium.
Taylor revealed Carsley had grown frustrated at being left on the substitutes’ bench after he had initially lost his place in the side due to tendonitis in his Achilles.
That ongoing injury issue, coupled with the form of Matthew Dudley and Alistair Waddecar, meant Carsley had found himself out of the starting XI.
Matters reached a head following the 2-0 defeat to Warrington Town on New Year’s Day – a fixture for which Carsley did not feature in the matchday squad.
“Brad wanted assurances that he would have the No.9 shirt,” said Taylor. “I wasn’t able to give him those assurances.
“I’m a manager who believes that if somebody is playing well in a shirt then you can’t just put somebody else straight back in.
“He was coming back from injury and we were trying to build him up fitness-wise. He had been used to being the main No.9 but you have to earn the right to the shirt.
“I wanted him to compete for the No.9 shirt so we are disappointed to see him go, but I respect his decision.”
Meanwhile, Taylor was pleased to see his men return to winning ways at the weekend after they suffered two successive defeats over the Christmas period.
On Boxing Day, they lost 2-1 at home to Marine and that preceded the loss to Warrington on the opening day of 2019.
It was looking like Brig were heading for another defeat on Saturday after they fell behind to an early penalty.
However, three goals in the final 12 minutes from Paul Dawson, Waddecar and Luca Navarro sealed the three points.
“We did not get the results that we wanted over Christmas,” said Taylor.
“We started off poorly against Marine on Boxing Day, but we came out for the second half, got a goal back, and I thought we were good for a draw.
“Against Warrington in the first half, I actually thought we could have gone in at half-time 2-0 up. Ally missed a penalty and their keeper made a worldy of a save.
“But Warrington came out second half and played some good football – they are a very good side.
“So it was good to get back to winning ways at the weekend. It was a great performance by the boys.
“It was a soft decision for their penalty to be fair. We stayed in it, changed the system in the last 20 minutes and got in behind them. We got the result we deserved.”
This weekend, Brig are at home to Hyde United.