Matt Derbyshire scored both goals in the first half at Elland Road to hand Forest a second consecutive victory for the first time since the start of February.
The result reignites hopes of finishing in the top six, with Forest now seventh in the table and just one point behind Brighton & Hove Albion.
"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," Brazil told reporters.
"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."
Forest face an away trip to Bournemouth on Saturday before a potentially crucial season finale against Brighton at the City Ground on May 3.