Hangeland was red-carded for a two-footed tackle on Cattermole on the half hour mark, with second-half strikes from Steven Fletcher, Carlos Cuellar and Stephan Sessegnon sealing only the second win of the season for Martin O'Neill's men.
Cattermole told Sky Sports 1: "At the time I thought it was two-footed and the rules say that you can't do that.
"It was unfortunate and not malicious. I don't think it was too bad but you can't do that."
"Every game's a tough game and we've found ourselves playing well but not getting the results we deserved. This was a massive game for us and we got the three points we deserved.
"We've got back to back home games now so it's something we can build on. We'll take a lot of confidence from that and keep working and try to climb the table.
Fletcher, who was scoring for the first time since September, added: "It was a relief to get a goal and get the three points. It's been coming.
"Sessegnon has been working very hard and he's been playing brilliantly so it's fantastic."