The umpire was standing against the goal post when a shot from Richmond's Matthew White struck him in the leg.
The ball rebounded off the umpire and was rushed through for a behind by Freo's Stephen Hill.
Tigers coach Damien Hardwick was furious after the match, believing the goal umpire was in the wrong place and should have called for a score review to check whether the ball crossed the line before striking him.
But Gieschen is happy with the way the umpire handled the situation.
"He was extremely confident, and that's the reason why he didn't call for a score review," Gieschen said on Monday.
"The goal umpire knew exactly where it hit him and where he was in relation to the line.
"The field umpire, who was down in a good position to see where it was as well, also believed it hadn't crossed the line, and there was a boundary umpire down there as well.
"So there was no doubt in any of the umpires' minds … (about whether) that ball had crossed the line. They all believed it hadn't – it stayed in play."
As for whether a video score review should have taken place anyway, Gieschen said: "Possibly, one of our score review people could've said, 'This is an interesting one, it 's quite close, let's have a look.'
"But they've only got a short period of time to make up their mind on that as well."
The incident at Patersons Stadium has ignited much discussion about whether goal umpires should be encouraged to straddle the goal-line or should stand further back.
The AFL's new general manager of football operations has asked Gieschen to look into it.
"I would think that first of all we need to get it so that the ball doesn't hit the umpire in the first place," Evans said on Monday morning.
"If the ball's rolling towards him, is there a position that the goal umpire can take so he doesn't actually come onto the field of play?"
But Gieschen is not convinced that a change is necessary.
"They do that because they want to try and adjudicate accurately touched balls on the line," he said.
"If they're not on the line people are going to say, 'Why aren't they on the line?'
"If they are on the line they run the risk of getting hit a few times and that's exactly what happened on the weekend."
The League is aiming to find a high-tech system to aid the goal umpires in the future.
Introducing two goal umpires has been thrown up as a stop-gap measure, but that has all but been ruled out.
"A goal umpire, right now, can be in the perfect position underneath the post and still not get that slight deflection off the post," Evans said.
"Having two goal umpires won't solve that; having two goal umpires won't solve whether the ball has been touched off the boot or touched in flight.
"It may assist as to whether the ball has crossed the line, but we need to try and progress towards a system – if we're going to spend money on a system – that eradicates this problem for supporters."
