The Serie A league leaders walked away from Ibrox with a 3-0 win thanks to second half goals Matteo Politano, Giacomo Raspadori and Tanguy Ndombele.
A fast start from the home side put the visitors on the back foot in the opening stages with an end to end feel to the game.
Spalletti saw his players handle that atmosphere and pressure, even if he was frustrated by the team's execution in the final third.
"We could have been intimidated after such a start from Rangers,” he said. “The Rangers fans are right on top of you and it feels like they are on the pitch with you. We were lucky as they had more danger in the penalty areas before the first goal.
"We knew how to use our weapons and we played, the opponents were physical and they put us in difficulty in the dirty situations of the match.
“Rangers hadn’t been in the Champions League for 12 years, so we knew they’d have this ferocious start to the match in a legendary stadium, but we held out, we played, we never lost sight of our objective and where we wanted to take this game.
“We did not use our quality enough in the final third during the first half, but then did it better after the break. What we did do was fight for every ball and we needed that here.”
After the opening day win over Liverpool, Spalletti knew how important victory at Ibrox was, while singling out Piotr Zielinski despite missing a penalty twice
"Failing to get three points would’ve been like handing back that advantage we earned," he said. “It was difficult, but the team never had doubts on the attitude to take.
“There were clear signs of growth, the reaction after the missed double penalty was very important. We kept hammering, because we saw a chance to get to the bottom in the right way.
"The presence of Politano on the spot is a symbol of depth and personality, Zielinski despite the two failed penalties was the best in the field.”