Both Edwards and Starkey announced their decision to leave Woodside Road last night, a club statement confirmed.
Edwards has struggled with injury over the past year or so and failed to hold down a starting place in Worthing's team this season.
Former Chelsea youth and Brighton & Hove Albion player Starkey has been a key part of Hinshelwood's side so far this term but made his intentions to move on known after Worthing's FA Cup win at Moneyfields on Saturday.
Hinshelwood said: "Ross (Edwards) has been really unfortunate with injuries for a while now, he just wants to get back enjoying football with his friends.
"I totally understand Ross' decision, if he ever wanted to come back and play a high level there could be an opportunity to do that with us. Ross started the first game of the season but seems to struggle getting through 90 minutes, cramping up and finding things difficult."
Starkey left the club under different circumstances. The ex-Brighton midfielder had a discussion with Hinshelwood following Saturday's FA Cup win, a match in which he was an unused substitute, and has now left the club.
"Jesse and I had a chat after the FA Cup win over Moneyfields, he wanted to know why he wasn't involved," Hinshelwood said.
"I told him that I went with the team I felt had the best chance of winning and he's now left the club.
"It's a bit disappointing but that was Jesse's decision."
Worthing boss Hinshelwood is not actively seeking to bring an outfield player in to replace the pair, looking to promote from the under-18s instead, if necessary.
He added: "I'm not sure what would be left in the playing budget with views to bringing anyone else in. Ricky (Aguiar) has come in this season and been excellent. There could be other opportunities for young players to come in, it's then about them taking their opportunity if and when it comes."
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