Chris Wood scored for Forest, which also saw James Ward-Prowse sent off late in the second-half. Chelsea found an equaliser through Madueke.
He later said: "They are a stubborn side. We went into the game with the intention to take three points but we couldn't get over the line and it's frustrating.
"They were defending pretty much the whole game and sometimes it just doesn't fall. We go into the international break and come back prepared for Liverpool.
"Credit to them, they are resilient with a lot of players behind the ball. They know if you give us space we are dangerous, having said that we could have scored three, four or five, but its one of those games."
On scoring the equaliser, Madueke added: "It's nice to get a goal, I've missed a few chances recently. Of course, we didn't win the game so it doesn't count for much.
"It's a good start, just one loss in the league, some great performances with a lot of goals and we're still conceding some sloppy goals. It's a good start with a new manager."
On being called up for England duty, he concluded: "It's an honour to be called up for your country and that your work is recognised so I'm buzzing."