"We are so happy to have Nigel Pearson come in," Doucoure told BT Sport after scoring on his 27th birthday.
"Everyone is pushing together, we are so proud of how we played.
"We deserved to win, we have had a fantastic week and we want to carry on and get out of the relegation zone."
Asked if Watford would survive, he added: "Yes, of course. Not a lot of people believe in us but we will fight to stay in the Premier League, and we will do it."
Watford boss Nigel Pearson told BBC Match of the Day: "We displayed a different kind of win today. We had to show a lot of commitment to dig in. It was a tough second half, going down to 10 men, Wolves are a decent side and had a lot of possession. But we were prepared to put our bodies on the line.
"What I've seen today is a group of players with incredible unity, they have an appetite to work hard to get out of the situation we are in."
On Christian Kabasele's red card: "The players feel it was harsh, based on the type of contact and the position of team-mates, so we will have to look at it. I've not seen it yet. The important thing was to try and keep calm, we had to make changes and I felt the players dealt with it exceptionally well."
Wolves boss Nuno Espirito Santo: "The performance was not the best. We started slow and allowed Watford into the game. They had a couple of chances but no more than that. But we only reacted after the second goal.
"We didn't create enough to really get the draw and get what we wanted. We have a team with character but we didn't have that today. Let's work on it and try and improve for the next one.
"We should improve, it makes a lot of difference when you take your chances as you can manage the game, especially when you have such a tight schedule."