Stephan El Shaarawy and Patrik Schick scored in the first half, and relegation-threatened Empoli's late equalizer was disallowed on video review as Roma held on to win 2-1 on Monday.
Captain Alessandro Florenzi was sent off 10 minutes from time — on his 28th birthday — following a second booking, and Empoli's Rade Krunic almost made the advantage count before the video assistant referee determined the ball hit Dimitri Oberlin in the arm just before the goal.
"The first match is over, and the best thing is the result," Ranieri said. "We have to work a lot, but we will always score sooner or later. We have to work instead on staying focused in order not to concede. It's not possible that we're letting in all these goals.
"These 90 minutes hasn't made me feel calmer, but I'm focused and positive."
Roma moved three points behind fourth-place Inter Milan, with the top four from Serie A qualifying for the Champions League. Empoli remained a point above the relegation zone.
Ranieri was appointed as interim coach on Friday, a day after Roma fired Eusebio Di Francesco following elimination from the Champions League and a derby defeat to Lazio. In charge of Roma from 2009-11, Ranieri was fired by Fulham of the Premier League on Feb. 28.
His second spell got off to a good start. El Shaarawy fired Roma in front in the ninth minute when he curled a stunning effort into the top right corner, but Empoli leveled in somewhat comical fashion three minutes later as Juan Jesus headed the ball into his own net under very little pressure.
Empoli almost immediately scored a second, but Manuel Pasqual's free kick bounced off the top left corner of the goal.
Roma took the lead again in the 33rd minute as Florenzi floated in a free kick from outside the right side of the penalty area and Schick headed it into the bottom left corner.
Empoli dominated as Roma's task was made harder by the list of players missing: Daniele De Rossi, Kostas Manolas, Lorenzo Pellegrini and Cengiz Under were all injured, and Edin Dzeko, Federico Fazio and Aleksandar Kolarov were suspended.
"It was a difficult match without many men seeing that the leaders were out — those who play 90 minutes, players who give a sense of direction to the play and the team," Ranieri said.
"I knew it would be difficult and I have to congratulate the team, which always remained compact even when we went down to 10 men."