The Evo-Stik South Premier Rebels caused a surprise as the Dolphins went down 2-1 at Arbour Park.
Hutchings had a game to forget between the posts as he left George Wells' winner slip through his grap.
Poole must watch this afternoon's FA Cup draw Come thought knowing they aren't involved.
But assistant manager Callum Brookes told the Daily Echo that they are right behind their goalkeeper.
"Nick was devastated by the mistake, as were all the lads," Brookes told the Echo.
“If someone had not followed an instruction or shown a lack of desire, you can start pointing fingers.
“But Nick would catch that ball 999 times out of 1,000. It was a clear-cut mistake, nobody does it on purpose and, ultimately, it cost us their second goal."
He added: “If you make a mistake as a keeper, ultimately, it can lead to a goal but I wasn’t going to start pointing the finger at him.
“Nick has kept us in loads of games over the couple of years I have been at the club."
Poole's focus now returns to getting back on track after a difficult first two months in the Vanarama National League South.
Tom Killick's side travel to Oxford City in a big game at the bottom of the table.