Bosnia forward Edin Dzeko was left on the bench for the side from the capital amid reports he is set for a move to Juventus.
Paulo Fonseca started in Verona with Henrikh Mkhitaryan and summer arrival Pedro.
At first dominating, Roma was soon put under pressure by Verona with Antonio Mirante deflecting an Adrien Tameze shot over the bar just before the break.
The post again saved the Roma goalkeeper from a Federico Dimarco effort with ten minutes to go, while Roma's Leonardo Spinazzola also rattled the post after 85 minutes.
"We can't say that it would have been any different with Dzeko," Fonseca, whose side hosts Juventus in its second game next weekend, said.
"We had a very good first half, missing four or five goals. Then in the second half we made a lot of mistakes.
"Had we scored in the first half it would have changed everything."