The Baggies were good value for their victory, even though it came courtesy of a late Saido Berahino spot-kick.
The hosts had the better chances and completely dominated after Debuchy was sent off for a two-footed challenge on Claudio Yacob just after the hour.
Pardew said: "I don't think we can have too many complaints.
"I think Mathieu has been our best player this last period, and he is an honest player. He genuinely went for the ball.
"There was no malicious intent, but you can't take off with too feet like that.
"We are going to suffer, and so will he. He will be a big miss for three games, and obviously it affected us today."
The spot-kick was awarded after goalkeeper Tim Krul - who was perhaps fortunate not to be sent off - tripped Matej Vydra four minutes from time.
Pardew said: "I thought it was a penalty. Fortunately the forward had a big touch, otherwise we might have lost another player.
"I thought the referee got that right.
"That was the deciding factor in a very tight game.
"I can't fault the players. I thought they were terrific in their application and attitude but with this programme, with 10 men, you're always going to be struggling.
"I thought it was a game we had good control over but unfortunately we couldn't get the breakthrough before the sending off. Obviously that changed the game."
- Sports & Recreation
- Claudio Yacob
- Saido Berahino