Mancini's first game back in charge of Inter saw Joel Obi score a second-half equaliser after Jeremy Menez's goal midway through the first half.
Given the limited preparation under his coaching, Mancini was pleased with the display put on by his team.
"Derbies are always difficult and that was the case today," he said.
"I'm very happy with how the team played, we changed a system that had been used for the last 18 months and it was never going to be easy. I'm happy, they all played well.
"I didn't think I'd revolutionise things in five days, it's only natural you have a few issues at the start. We're a long way off third place but it's too soon to be looking at the table.
"Our aim is to win as many games as possible even though we're not 100 per cent."
Inter sit ninth in Serie A after managing to win just four of their opening 12 league matches, but they are only five points adrift of third-placed Napoli.
Mancini said he understood his team would initially struggle with a change of tactics, but believes they will be suited to playing four at the back.
"We had some understandable difficulties with the three up front," he said.
"They had to work hard defensively and they still need to improve their movement but we can move forward through hard work.
"It might take some time to master a back four but we have players in the squad who play that system with their national teams. We definitely have to improve."