Wolves began the game strongly and went in two goals ahead at the break as Helder Costa and Ivan Cavaleiro scored the goals.
The game turned in the second half as Wolves had Ruben Neves and Matt Doherty sent off, both for second bookable offences.
Middlesbrough applied the pressure but, although Patrick Bamford scored a late consolation, Wolves held on to secure an heroic 2-1 victory.
Coady praised all of the Wolves players for their character they showed in earning the victory.
“It was a game where if we’re looking back with 11 men, we were fantastic,” said Coady.
“First half, we dictated the play and scored two fantastic goals and I thought we were on top at the start of the second half as well.
“The way we played, I thought, was really good.
“To show the character we did, we’ve done it all season, the gaffer instills it in us every day and we’ve done the same again.
“We had to dig in: I thought the boys were brilliant, the boys who came on did the job properly and I thought we deserved the points in the end, I really, really do!
“We know that we’re good when we go forward and we score lots of goals - we’ve got some fantastic attacking talent.
“We’re good when we’ve got the ball in their half as well.
“Obviously, Ruben’s (Neves) red card changed the game but I thought in the end, we deserved the three points.”
Wolves were forced to play for over half an hour with 10 men, and then over 20 minutes with nine men!
Coady said that Wolves were always confident that they could see the game out, claiming it is a huge result for the football club.
“You’ve got to be confident that you can see it through” Coady continued, “we’ve kept lots of clean sheets this year and it was about organisation whether you’ve got 10, 9, 8 whatever it is!
“You need to just dig in and make sure you come away with a win and we’ve done that tonight.
“Their goal was fantastic - he’s put it in the only place that he could do.
“We’re disappointed with that but in the end it’s a huge result for the football club.
“It was brilliant, it was something that we had to do - everybody dug in, it wasn’t just the back five, John Ruddy, it was everybody.
“I thought we saw it out fantastically well in the end.
“You’ve seen with the crowd at the end, it was incredible to share that with everybody involved and like I said it was a huge result for the football club.”
Wolves now face Hull City at Molineux in the Sky Bet Championship on Tuesday (7:45pm).
Coady revealed that Nuno retained the player’s concentration soley on Tuesday’s clash against Hull.
“The manager’s just told us that there’s a long, long way to go,” said Coady.
“There’s seven games to go, there’s games where we have to still win to move forward.
“We’ve got a little bit of momentum at the minute and as long as we’re playing well and doing what the manager says week in, week out, hopefully we’ll be ok.
“It’s a tough place to come - I’ve been here plenty of times now and I’ve never really got anything here.
“It’s such a tough place to come, the crowd really get behind them.
“The boys dug in really well tonight and we’re going into games with confidence at the minute.
“We’ve got some fantastic players on the pitch who play some great football.
“It’s up to us to keep improving, it’s now on to Hull and we’ll hopefully get better.”