Afterwards Keane was far from ecstatic, but admitted it was a relief to get off the mark.
"I'm pleased, it's better than losing and it's always nice to win football matches," he said. "It's ironic because I don't think we played particularly well.
"Having said that, for four or five weeks I've been saying how well we've played without getting the rewards.
"Today we huffed and puffed and won an ugly match 1-0. Sometimes that's what you have to do in football. That's allowed.
"We'll be back working hard on Monday morning, though, and anyone who thinks we're going to relax after winning one game in 15 obviously doesn't know me very well."
Keane feared the worst when Bryan Hughes had a golden late chance for the Rams.
However, he shot over from an excellent position and Keane added: "I was concerned when it fell to Bryan Hughes.
"He's a very good, technical player but if we'd conceded again it would have been hard to take. We made hard work of it and could have killed the game off.
"Tamas (Priskin) had a great chance, one-on-one and right in front of goal, but credit to their goalkeeper for making the save."
Wright headed the only goal after 66 minutes when he rose amid a pack of players and headed home a right-wing cross from Grant Leadbitter.
Derby boss Nigel Clough felt his side deserved more from the game and admitted he considered trying to get the game called off due to their crippling injury list.
"We were looking into that but obviously if we can get a team out there that's what we have to try and do," said Clough, who has 16 players on the sidelines and could only name five on the bench.
"If at all possible the authorities want you to play the game and we've done that. We don't like calling games off and had faith in the players we had out there to put on a performance and they did that.
"It's a defeat, but it's an encouraging one. I thought we did enough to get something from the game but when you're on a little run like we are things can go against you.
"It was an extremely spirited performance, given we were down to the bare bones, and bitterly disappointing that we should come in on the wrong end of a defeat.
"Bryan Hughes had a very good chance at the far post, their goalkeeper had a very good game and it was a case of the ball not dropping for us at the right times."
Despite his disappointment, Clough said: "I'm delighted for Roy (Keane).
If we were going to lose to anyone I'm glad it was him."
The pair were team-mates at Nottingham Forest.