The former Tranmere Rovers winger joined the League Two side in March after being released by the Rovers after he failed to make a single appearance for the club last season.
Speaking to the club's website, Clarke said: "I wish Abdulai all the best in the future but it just didn't work for him here.
According to westerndailypress.co.uk
Angelo Balanta and Abdulai Bell-Baggie also both turned down the offer of new deals and Clarke said it is disappointing losing the pair.
"They were both offered short-term deals because I thought those were the sort of terms that were right for the football club. I look at Angelo and I know that with a good pre-season under his belt they could be a really good player there.
“Abdulai didn't play for us when he came in at the tail-end of last season, so he wasn't tried and tested. I'm not the sort of manager who wants to gamble on handing out silly long contracts until I am sure they will return some value for money. “
He continued: "The two lads were not offered great deals by any stretch of the imagination, but at the same time I felt they both still had something to prove. The players got their offers and it was their right to either accept them or turn them down. What is important from my point of view is that whatever decisions are made, we must move on quickly.”