I connected my Lego Dimensions PS3 toy pad to an Xbox One because I thought it would work there too! Unfortunately it didn't! Do I have to fear now that it is broken?
No you don't have to
Then why should it be broken? It just does not work on a device for which it was not designed. As simple as that.
So it's not broken, it just doesn't work on the Xbox?
Yes it could have been that it broke!
Exactly
No.