Stefano Pioli hailed Inter's "heart and soul" after beginning his reign with a last-gasp 2-2 draw against city rivals AC Milan.
Ivan Perisic popped up in stoppage time to snatch a point for the Nerazzurri, after Suso had twice given Milan the lead.
Antonio Candreva thumped home the goal of the game in the second half to cancel out the Spanish winger's opener and Inter dominated for large parts.
However, while encouraged by the spirit shown by his team, Pioli sees much room for improvement.
"I don't think we deserved defeat considering the performance, but we still have to improve in many areas," he told Mediaset Premium.
"I tried to give some balance to the team. We allowed a few too many counters in the first half because the preventative marking wasn't always done correctly.
"We needed organisation and balance. I asked the team to put in heart and soul, which I think the boys did tonight."
Candreva, a key player in Pioli's Lazio side before joining Inter this season, believed victory would have been deserved for the Nerazzurri.
"A fine derby from us, we deserved the victory and achieved the point with merit," Candreva told Mediaset Premium.
"The two Milan goals were both counter-attacks, so we need to improve on our defending.
"We are Inter, we have to be in the top spots of the table. Now we need to climb back up and improve by using this performance as the foundation, because it was a great match."
