The cup win comes ten days after Bremen lost the UEFA Cup final at the hands of Shakhtar Donetsk, and Schaaf is happy their season was concluded with a happy ending.
"It was a great game from both teams, but you saw that we wanted to win the cup," Schaaf said after the final.
Midfielder Mesut Ozil scored the only goal of the game with a left-footed strike right after the interval.
"A fantastic player in Mesut Oezil is often not rewarded because he doesn’t always shoot.
"I was delighted with his goal. He has shown great development and still has a lot in him. For what he has achieved this season, I compliment him."
The trophy is the fifth for Bremen under the guidance of current coach Thomas Schaaf.
The 48-year-old won two German Cups, one League Cup and a Bundesliga title since he took over Bremen in 1999.