Gluing the 'felt' only will result in the 'cutout' areas being subject to stretching if someone presses on the areas.
When gluing my cuttings to felt I always apply the felt to some other material, cardboard or thin plywood first and then to the back of the cutting.
In this particular case i would coat a piece of 1/8" BB with a dark stain, spray with lacquer and then glue the felt to that with Alene's Tacky Spray glue and let dry.
Then I would spray the back side of the piece with the spray glue and place it on the face of the felt and use weight to press the two together for at least 30 minutes.
That is MY way, not the ONLY way....
~~~GB~~~