Murphy netted twice in the first half, with Aaron Cresswell also scoring and providing three assists as the Suffolk side appeared to be out of sight.
However, three goals, with two from Craig Bryson, saw Derby level before the end and Murphy told the Ipswich Town website of the distinct change in mood.
He said: "It's great to have scored tonight but I should be standing here on a high after a win but we're all feeling very flat tonight.
"We should have had the game wrapped up after our first-half display but we've allowed Derby a way back into the game, which they've took and we're disappointed to have dropped two points."
Ipswich next face Sheffield Wednesday away on Saturday.