Dortmund had a chance to go four points clear but were outclassed, down 3-0 after 23 minutes and 4-0 down early in the second half, before scoring two late consolation goals.
"We just made up 10 points in eight games and now (Bayern's lead) is only two. There's no depression in Dortmund, if there is then there shouldn't be. We'll be back," the teenage English midfielder told the Bundesliga website after the match.
Former Liverpool and Juventus midfielder Emre Can - who has been in stellar form for Dortmund who won nine and drew one of 10 league matches to start 2023 before the Bayern defeat - echoed Bellingham's comments: "The league is not finished yet. They are two points in front of us. We will see what happens."
Dortmund manager Edin Terzic too, said his "disappointed" team would fight on.