Simone Inzaghi believes Inter deserved all three points in their 1-1 derby draw with Milan on Sunday.
Hakan Calhanoglu – who joined the blue half of Milan from the red side on a free transfer in July – won and then converted an early spot-kick to put the Rossoneri ahead.
The Turkey international became the fourth player to score in his first Milan derby in Serie A after having played the previous encounter with the opposing team (since 1994-95), after Hernan Crespo (2006), Ronaldo (2007) and Zlatan Ibrahimovic (2010).
Inter were pegged back soon after as Stefan de Vrij scored an own goal – the first in a Milan derby since Samir Handanovic's in December 2017.
The Nerazzurri were handed a second penalty in the first half, but Ciprian Tatarusanu saved Lautaro Martinez's strike from 12 yards to keep his side level.
Martinez has now missed three of the last six penalties he has taken in all competitions for Inter.
"The glass is half-empty because we had so many chances and missed a penalty, so in my view we deserved far more," Inzaghi told DAZN.
"We were up against a great team who are deservedly [joint-] top of the table. We're behind them in terms of progress, but there is time to get back on track and performances like this will give us confidence.
"Over the past six games we drew with Juventus and Milan when we probably deserved to win. Milan and Napoli are keeping up a remarkable tempo, but there's a long way to go and we are up there.
"We wanted to give our fans a victory and I feel we did enough to deserve it. The tempo was very high and both teams probably could have done a lot better on a technical level, but it was intense.
"Milan are a very technical side, so you have to tire them out, make them move. We did well in the opening 20 minutes and generally I think we deserved more, we only struggled a little in the final 15 minutes."
Despite Calhanoglu having already scored from the spot, Inzaghi said he had no issues with Martinez stepping up to – unsuccessfully – take Inter's second penalty of the game.
"Our penalty takers are Martinez and Calhanoglu, while Ivan Perisic can take them too," the head coach added. "Hakan asked to take the first, Lautaro took the second.
"It's between them to decide, we know how those moments work."
Inzaghi also provided an update on Nicolo Barella, Edin Dzeko and Alessandro Bastoni, who were substituted with apparent injuries in the second half.
"Barella felt a twinge and asked for the substitution," he explained. "I had a few issues with Dzeko and Bastoni in the first half, so naturally playing with this tempo and so often, the muscles are under strain. Hopefully they are nothing serious."