The result - Forest's first win in 13 league outings - lifted them to within three points of sixth-placed Brighton and, while they still need other sides to slip up, Brazil wants his side to pile the pressure on the teams above them by securing another three points at Elland Road
"I said weeks ago that it might not take a massive number of points to get you into sixth place, and it is proving to be the case," he said after seeing Matt Derbyshire's second-minute goal clinch the points at the City Ground.
"If we can get a win at Elland Road, the last two games are going to be very interesting.
"I am really pleased for everyone at the club, because this has been a tough period. To get ourselves a win now gives us some momentum - but we have to carry that on now, on Monday afternoon.
"That was more like a City Ground performance. To a man, we wanted to fight hard for this."
Brazil believes putting an end to their costly run of form - which had seen them last win on February 11 at Huddersfield - can prove a massive lift.
"It feels better in the changing room for the players - but this was one for the fans," he said. "It has been a long time since they have seen a win.
"I have been frustrated with the home performances since I took over, but our intensity was good. We played some good football and should have been more than a goal up by half-time.
"The frustration was that we did not make enough of the chances we had. But no complaints, because we had some big performances from a number of players. We will go up to Elland Road and try to reproduce that."
Birmingham boss Lee Clark urged his players to remember that their relegation fate remained in their own hands, as they headed into three consecutive home games with their Championship status still at risk.
And he called on his side to perform to the same level as they did in the second half at the City Ground, when they almost forced an equaliser.
"We have to dust ourselves down following this, because we have some huge games coming up," said Clark, with his side now a point off the drop zone.
"We have to go again now. We need our senior players to step up to the plate now.
"It is in our own hands and we have to look after ourselves now - we have to produce the goods. We grasped things better in the second half - but we need to do it for entire games."
Clark felt Birmingham had done enough to take a point, with Paul Robinson and Chris Burke coming close to equalising.
"We are disappointed not to come away with a point. In the second half we were much better and felt we deserved something from the game," he said. "The goal was down to our poor play."