Elliott cancelled out Chris Brandon's opening goal and Aaron Wilbraham netted the City winner three minutes after coming on as a half-time substitute.
However, the prospect of being without talisman Elliott left Taylor frustrated.
"We know he's got a fractured cheekbone and we're really disappointed because 23 goals is a great return and he looks like he could have broken the club record," said Taylor.
"We were disappointed with the challenge, because the players said they thought an elbow had been used, but I don't know who their player was, and we'll have to get on with it.
"We've showed tremendous character again today and hunger is not a problem for us."
Huddersfield manager Peter Jackson admitted: "This season we have never played well for 90 minutes and we have only played well in patches.
"I thought we were excellent for the first 45 minutes but then gave away a sloppy goal. We have been too inconsistent this season."
Huddersfield struggled to hang onto the ball in the opening half, but with Efe Sodje a giant at the back, Hull were having little luck in front of goal.
Home goalkeeper Boaz Myhill produced an outstanding save to deny John McAliskey, but the visitors did break the deadlock five minutes before half time.
McAliskey cleverly found Brandon, who wrong-footed the goalkeeper before slotting home left footed.
The lead lasted just two minutes though, as Elliott drilled home a left-footed shot through the legs of the goalkeeper after playing a neat one-two with Delroy Facey.
Just three minutes after coming off the bench for Jon Walters, Wilbraham notched the winner.
On-loan defender Stevland Angus raced forward down the right and crossed early for Wilbraham to head home his first goal for Hull since signing from Stockport in the summer.