Clinical Welbeck blasted the Gunners into a 2-0 lead and once Alexis Sanchez had stretched the advantage further, the £16million signing from Manchester United added his third as the Turkish club were swept aside at the Emirates Stadium.
The only blot on an otherwise fine night was the red card shown to goalkeeper Wojciech Szczesny for bringing down Burak Yilmaz, who rifled home from the spot.
"Danny was on the end of good movements
It's good that slowly he gains confidence and finishes well
Hopefully the hat-trick will help him gain confidence," Wenger said.
"It always helps to know that you have a chance to play in the next game
That gives you confidence.
"What is good for me is that his team play is good as well
His team work and work rate are good.
"It's not just his finishing because he wants to help the team.
"I believe that, technically, he's very sound
I was a surprised that he's technically clean and that he's a good passer of the ball.
"And I didn't know he was so quick
Honestly, I knew he was quick but he can be electric when he starts - he has great pace."
Sanchez was the victim of a two-footed tackle by Felipe Melo in the first half that Wenger felt should have been punished by a red card.
The Chile international appeared to be upset when he was eventually substituted by Wenger.
"Yes it could have been a red, although I'll have to see it again
My first impression was that it was a red card," Wenger said.
"When we went down to 10 men I took him out because I wanted us to be more solid defensively.
"Fortunately in my life I haven't met many players who were happy to come off.
"We had good pace on our game and the transitions were good
Danny was at the end of good collective movements.
"We had a good start and they were surprised by our pace
We lost control of the game when we went down to 10 men.
"As soon as we allowed Galatasaray to play, they became a dangerous team
But for an hour maybe our pace was a problem for them."
Wenger refused to condemn the rash challenge that resulted in a red card for Szczesny.
"We lost the ball, an unnecessary mistake in our own half, and after that it was a through-ball," Wenger said.
"I saw him coming out and I thought he may have read the situation well.
"He tried to come out and was a fraction late so he conceded the penalty
It can happen.
"I think the fact is that we're more guilty of losing the ball in our own half - it can be dangerous and we didn't defend too well on that front."
Source : PA