Giroud was dismissed early in the second half at the Emirates Stadium for head-butting Nedum Onuoha right in front of referee Martin Atkinson and Wenger gave his forward an icy glare as he stalked off the pitch.
Arsenal, who had opened the scoring through Alexis Sanchez, added a second through Tomas Rosicky but faced a nervy finish when Charlie Austin pulled one back from the penalty spot.
"It was a deserved red card
Madness is a strong word - he didn't kill him
But he touched him and should not have done it
He should have been in control," said Wenger, who confirmed that Giroud has apologised.
"Olivier Giroud knows he made a mistake and I know him well enough to think that he will not do it again.
"He told me he was pushed in the back and that projected him into the keeper
Usually he's a guy who's in control of his response."
Giroud now begins a three-match suspension that includes Premier League appointments with West Ham and Southampton and the FA Cup tie against Stoke City.
"Honestly, you never need that
In my job you sometimes have to deal with the strengths and sometimes the mistakes of people," Wenger said.
Wenger celebrated his 400th Premier League victory and 600th as Arsenal manager, but was almost denied the milestones when QPR poured forward in the closing minutes.
"We were nervous and the opponent pushed forward
Our game is about psychology and the mental aspect
In the final part of the game when the result is not settled, it's always very important," Wenger said.
"I'm happy I could win 400 and it's not as easy as it looks
The next 400 will be much more difficult!"
Sanchez missed an early penalty, awarded after he had been tripped by Armand Traore, and QPR's defending was feeble throughout.
QPR boss Harry Redknapp described Traore's defending for Sanchez's opener as "atrocious" but Rangers were denied a second spot-kick after Kieran Gibbs tackled Bobby Zamora without the ball.
"It was a blatant penalty
I've looked at that and when Bobby came in he couldn't believe he didn't get the decision
It was a penalty
He got dragged down," Redknapp said.
"It wasn't until we got back to 2-1 that we suddenly started to take the game to them
I felt we weren't positive enough at 1-0 against 10 men
For them to score was the worst possible thing
To go two down was a massive blow.
"You have to come away with something
This was a good opportunity against 10 men to pick up a point here
We've got two home games now (against Crystal Palace and Swansea) and we have to pick up some points in those."
Source : PA