Derbyshire scored the winner against Birmingham on Saturday and his two goals in the opening 16 minutes at Leeds were enough to earn three more points from a 2-0 win that left Forest one place and a point outside the top six.
The striker has started only six games this season but Brazil said: "Matt has had the opportunity and grabbed it.
"He has done really well on the training ground and I think he has a very positive mentality which is vitally important for any striker.
"He runs into spaces behind the opposition's back four which is encouraging for us because it frightens the life out of the opposition. He is performing at a very high level at this moment in time."
Brazil added: "I was very pleased with our performance.
"After going two up we handled everything Leeds could throw at us and defended like men. I was very impressed and proud of them.
"The two clean sheets over Easter have been massive for us.
"We have turned the situation round nicely in the last 72 hours but we need to settle down now and see what we can achieve at Bournemouth and give it a good go.
"Matt will get the plaudits but we have a group of players fighting for the cause."
Leeds boss Brian McDermott has a list of players he would like to bring in over the summer to strengthen a squad that has failed to challenge for the play-offs this season.
New owner Massimo Cellino is currently abroad but McDermott is planning a meeting with him to discuss recruitment strategy when he returns.
McDermott said: "We definitely need to look at bringing players in and making changes to the squad. I have a list of targets and we have to try and do the deals. I will have a meeting with Massimo when he returns this week.
"We have seen that kind of performance too many times this season and it is something we have to address in the summer. We have to make sure the squad is up for the challenge of next season."
The game was just one minute and 32 seconds old when the ball was threaded through the centre of the Leeds defence to Derbyshire, who picked his spot.
The lead doubled when Derbyshire took advantage of a slip-up by Leeds defender Scott Wootton by clipping an angled shot past Jack Butland from 12 yards.
Forest replaced limping keeper Dorus De Vries with Bulgarian Dimitar Evtimov 10 minutes from the end and he saved Smith's stoppage-time header.