Midfielders Nenad Milijas and Cadu scored either side of halftime as Red Star fans lit dozens of flares at their Marakana stadium to celebrate the goals.
"I've never seen an (atmosphere) like this, I will take home great memories from my debut here," Sa Pinto told reporters.
"I can say we had good fans in my time as a player and coach at Sporting but this was unbelievable and I really wish for a full house in our next home game.
"There is still plenty of room for improvement and we must work harder to be quicker in moving the ball forward and creating space because we didn't quite excel in that department this evening."
The result moved second-placed Red Star to 41 points, eight behind champions and leaders Partizan Belgrade who visit struggling Hajduk Kula on Sunday and are on course to win a record sixth successive league title.
Brazilian Cadu scored his first goal of the season on the stroke of halftime when he took the ball in his stride and unleashed a first-time shot into the top corner.
Milijas sealed victory by scoring Red Star's 4000th league goal but his feat was marred by a clash of heads with an opponent that forced him to stagger off the pitch in the closing stages.