A late Mario Balotelli penalty earned a 1-0 triumph over Hellas Verona at the San Siro as Milan recovered from their shock defeat to Sassuolo in their last league match to earn only a third Serie A win in 12 games.
Seedorf, who recently replaced Massimiliano Allegri in the Milan hotseat, said to Gazzetta dello Sport: "This victory is certainly dedicated to all the Milan fans.
"I am happy for the squad, as there is a lot of work to do and a win helps to make it all feel easier.
"We didn't have much time to prepare for this game over the last few days, but the players did very well to put pressure on Hellas and to keep our rivals in their own half.
"Although we won thanks to a penalty, I still believe we deserved the win considering our overall performance.
"After the game, we formed a circle all together in the locker room and I said we would do the same after every game, whether it is a win or a defeat, so we can all look each other in the eye.
"We are all responsible for every result."
Seedorf, 37, had been playing for Brazilian side Botafogo before retiring last week to accept an offer to lead Milan, a club he played for for 10 years.
The former Holland international took over the reins from Allegri, who was sacked with the club 30 points behind Serie A leaders Juventus.
"The club president (Silvio Berlusconi) and (club administrator) Adriano Galliani showed courage to make this decision," Seedorf said of his appointment.
"I felt ready for this position and received a wonderful letter from (Holland coach) Louis van Gaal, who helped construct the management course for me, so I am learning fast.
"I am focused on what we want to develop next week, which will be the first real week to get training done and concentrate on all the aspects of building the game I've got in mind.
"Right now, we want to focus on rediscovering the joy of playing football and training with the ball."
The Rossoneri climbed to 11th place with the victory and are seven points behind fifth place after 20 games.
Milan travel to Sardinia to face Cagliari on Sunday.