Bombers fans were irate when Kyle Hardingham was penalised for holding the ball late in the final quarter, despite appearing to handball when tackled.
Swan Jude Bolton took the free and kicked a goal, putting Sydney in front by five points.
Gieschen said on Tuesday that the umpire's call was a good one.
"When they've had prior opportunity, they must handball it or kick it correctly," Gieschen told afl.com.au.
"In this case with Hardingham, the ball bobbled up and then he punched it away with his fist, so it didn't constitute a handball.
"In actual fact, it's a fantastic decision.
"You don't like to see any team lose over a free kick, but in this case it was a correct free kick and if we hadn't applied it, Sydney could rightfully feel that they were hard done by because he didn't dispose of the ball correctly."
A short time later, with the ball deep in the Bombers' forward line, Brent Stanton went to ground with Sydney's Martin Mattner at his back.
A free kick would have given Stanton a shot on goal to put Essendon back in front with less than two minutes remaining, but play was allowed to continue.
Again, Gieschen backed the umpire.
"(Mattner) didn't cause him to go to ground, Stanton dropped his knees and was heading towards ground," the umpires boss said.
"From there, the Sydney player has to be very careful not to land in his back, not to push him in the back with his hands, and we think he did that.
"We can see contact, but that contact is through his backside and down through his legs.
"So it wasn't a push in the back, and we were very comfortable that the umpire called play on in that situation."
Gieschen did, however, once again admit that Richmond's Luke McGuane should not have been penalised for a deliberate rushed behind on Friday night.
He also said a boundary umpire's decision to call for a throw-in when Hawthorn's Stephen Gilham played on from outside the field of play against Melbourne was wrong.
"Our boundary umpire…just probably didn't process it properly, just a little bit over-zealous and felt that because (Gilham) took those two or three steps running outside the boundary line, that he'd actually played on," Gieschen explained.
"But under the interpretation of that one he's more than entitled to take the mark and play on provided he heads in the one direction.
"So Hawthorn were stiff in this situation. He should have been able to continue."
