Derby failed to win a match in the Premier League last season after Jewell took over as manager and have won seven of their 26 Championship fixtures so far this season.
Hutchings will be at the helm for Saturday's FA Cup third round tie at Forest Green Rovers and that big clash with United in the first leg of the Carling Cup semi at Pride Park on 7 January.
Derby chairman of football Adam Pearson told BBC Radio Derby that the club had not put any pressure to quit on Jewell, who arrived at Pride Park after six months out of the game following his departure as boss of Wigan Athletic.
"It was probably one result too far for Paul," said Pearson. "He came to see me after the game and said that he felt it just wasn't working out and didn't want to club to suffer as a result.
"He just feels that the club needs a fresh impetus and a new direction.
"So we agreed a deal to go our separate ways, which is something entirely private between the club and Paul."
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