Henry's challenge in the 86th minute went unpunished but Routledge was sent off by referee Anthony Taylor for his reaction to the Rangers midfielder.
Swans substitute Wilfried Bony went on to score an injury-time equaliser, cancelling out Leroy Fer's first-half strike, but Monk was still seething at Henry's challenge after the match.
"It's a leg breaker," Monk said.
"I think everyone knew in the stadium apart from the official and then the double whammy of our player getting sent off for apparently kicking out.
"He doesn't kick out at all
I just hope justice is done not just for us but for football in itself.
"I'm losing a bit of faith
It's hard for us to keep faith when we continually have decisions like this, big moments within games.
"That sounds like me moaning, I'm not at all
I'm just telling you the facts.
"I hope the red card gets rescinded because that will 100 per cent be the right thing to happen.
"We'll be appealing for sure
My player goes from nearly having his leg broken to getting sent off, I don't see how that can happen."
QPR were lucky not to be reduced to 10 men themselves when goalkeeper Rob Green stopped Routledge going through by handling the ball outside the area in the sixth minute with the score still 0-0.
"It's half a metre outside the area, the linesman has a clear view of it," Monk said.
"I don't see how he misses that but we seem to be getting a lot of people missing things throughout the season.
"I'm tired of talking about these things
It's time for you guys to write about it, that's the only way it can be sorted out.
"It's difficult for me, my players and the club because we're suffering a lot in these situations."
Bony, whose goal was his ninth of the season, is reportedly attracting interest from Manchester City but Monk insists the decision not to start his star striker was purely down to fatigue
"There's been a lot of games in this period, that's why I wanted to rotate the squad," he said.
"I thought Bafetimbi (Gomis) was fantastic today and the game opened up towards the end so I put Bony on and he showed his professionalism and concentration to get the equaliser for us."
On City's interest, Monk added: "It's speculation, there's nothing concrete.
"I think you can see today from when Wilfried came on, he showed his focus for our club and respect to the players and the staff
That was in his performance.
"To say his mind is elsewhere, is clearly not true, he's actually very focused on doing well for Swansea."
The draw means QPR extend their unbeaten run at home to seven matches but Harry Redknapp was disappointed his side were unable to hang on for all three points.
"They were two more vital points today we deserved and we needed but we couldn't hang on for," Redknapp said.
"It's only a minute and a half to go, we've defended for our lives and to concede then was obviously a big blow for us."
Redknapp added: " We needed a second goal but when they put three minutes up, you think we just have to get it in the right areas, play down the sides
"We had a good opportunity and we could have killed them off really."
Source : PA