"It was fantastic to captain the team, and I think it was a good result and a good performance," the 22-year-old, who completed 70 minutes and looks sharp in time for the visit to Anfield this weekend, told manutd.com.
United's Champions League ambitions are now on hold until late February when the knockout matches kick in, but Rooney is unambiguous in his aims.
"We'd love to win the Champions League this season," he said. "Hopefully we can go one step further than last year and reach the final."
The United front man was impressed with the performance in Rome, particularly from the young players.
"It's a great experience for them to get Champions League football under their belts," he said. "I'm sure it will have helped them a lot. Pique, Evans and Simmo did really well. They have great ability and bright futures ahead.
"As a team I thought we did very well and got off to a great start, putting them under a lot of pressure. Gerard Pique scored a great goal and we had a couple of chances in the second half to win it. We kept going after they scored and in the end a draw was probably a fair result."