The visitors held on for a 0-0 draw at Molineux after Cattermole was sent off after 62 minutes for collecting two yellow cards in just 54 seconds.
It was a second straight away clean sheet for Coleman’s side but they remain second bottom of the Sky Bet Championship, although are just a point away from the safety line.
An excellent defensive performance frustrated Wolves and Coleman hailed their heroics after a 3-1 defeat to Reading last week.
He said: “I told the players there were two things they could do, duck it or face it. I wouldn’t advise ducking it because, even if you don’t get what you want, at least you have a bit of peace of mind if you face the challenge.
“After last week where everything’s going right and then we have a man sent off and end up losing 3-1 you could easily come here and crumble but we didn’t do that.
“We have eight or nine players unavailable but it’s about the boys who are available, ready and standing up for themselves and that’s what they did.”
The former Wales manager refused to blame Cattermole or the officials for the midfielder’s ninth career red card for quickfire fouls on Romain Saiss and Diogo Jota.
He said: “The first one, you see tackles like that quite a lot and they don’t always get punished but he got the yellow and that was unfortunate. The second one, I can understand. I’m not going to criticise the officials. For us, the timing of it was a big test.”
Robbin Ruiter made two smart saves from Jota and Ivan Cavaleiro but in-form Wolves failed to create clear openings.
They missed the chance for a seventh straight win but did extend their lead at the top of the Sky Bet Championship to five points, although Cardiff play their game in hand at Reading on Monday.
Boss Nuno Espirito Santo said: “It is disappointing because it is not the result we wanted but frustration, no, it is part of football.
“Victories are hard to achieve and we work hard to achieve that. The boys did everything. They kept trying. There was only one team looking for the three points.
“But I am not not frustrated and I’m conscious games like this will happen again and we have to find solutions. I’m not worried about the game plans of opponents.”