Reijnders scored in the 3-0 midweek win at San Siro stadium.
“Milan is red and black because Inter couldn’t beat us once this season,” Reijnders told Gazzetta.
“We showed what we are capable of. The last one was the best of the five derbies played. We haven’t been consistent enough in terms of performance and dropped points along the way.
“Winning the Coppa Italia would allow us to take part in European competitions next season and we must go for it. We were like hungry dogs out there and on top of that, we showed the quality that hasn’t always been there this season.
“There’s no real explanation, other than we were not consistent. A clear example is winning at the Bernabeu and then drawing in Cagliari. If you want to fight for the title, you can’t afford that.”
"Milan is a dream"
On signing a new contract just weeks ago, Reijnders added: “Living in Italy and playing for a club like Milan is a dream I’ve had since I was a kid. My family is happy here.
“When I was offered a contract extension, it was a no-brainer. I want to thank the club: the management moved quickly to reach an agreement.”