Alberto Aquilani struck midway through the first-half before three goals in the final ten minutes settled the match. An own goal from Falcone, Francesco Totti's wonder-strike and an injury-time effort from Mirko Vucinic rounded off the scoring for Roma.
"This game with Parma may have looked easy, but that was down to how well the lads played," said Spalletti afterwards. "We proved that we are in good shape physically as well, so now all we need to do is lift the pressure and mood for the Real Madrid match.
"The second leg at the Bernabeu is a great opportunity to prove what we're made of.
"If we play like we did today, then we can certainly walk with our heads held high."
Totti was handed the captain's armband by Roma legend Giacomo Losi, whose record of Serie A appearances for the club was broken this week.
"This was a feeling I will carry with me for my whole life," smiled an emotional Totti after his 388th game.
"I remained at Roma, the club I have always supported, and it is a challenge I have been able to win."