Juan scored the only goal to defeat Bari 1-0 at the Olimpico and Francesco Totti had a penalty saved.
"We really needed these three points," said Ranieri. "The glass is half-full, as we kept a clean sheet, but also struggled to find Totti and Jeremy Menez between the lines.
"When we did manage that, then we made life difficult for Bari. We did some good things today, so that will do in the circumstances."
The Giallorossi had picked up one point from their last two Serie A games and conceded a late equaliser at Cluj in the Champions League.
"Conceding so many late goals and comebacks did create a bit of tension," confessed Ranieri.
"We had a completely revamped midfield today because Daniele De Rossi was suspended and David Pizarro not 100 per cent fit. When he is 100 per cent, then he will play, there is absolutely no controversy to be found here."