It’s strictly the present tense; if the same state of mind had to be described as situated in the past you’d have to say “j’étais désolé” or “j’ai été désolé“; that is so insofar as the most basic form for the past is concerned. Time correspondences can indicate other past forms and the literary style gives the option of using “je fus désolé“.

• Je suis désolé qu’il ait échoué. (L’échec date d’un jour quelconque dans le passé par rapport au moment où la personne parle mais la personne qui parle est désolée au moment où elle parle.)

“Désolé” has nothing to do with a past participle, it’s simply an adjective in this context; for this reason “suis” can’t be a conjugated form of the auxiliary “être” and it is therefore the plain verb “être” meaning “to have the caracteristic expressed by the adjective or noun that follows”.

The question of this state of mind being a feeling or not does not impinge upon the tense in the past. The tense is determined solely by the narrator’s point of view towards the action or state of affairs related by the verb. If he/she doesn’t need or doesn’t want to make precise that this action is limited in the past he/she uses the imparfait”.

• Il était désolé, il n’y avait plus de café ni de thé. (He was that way and possibly he still is.)

• Il a été désolé pendant un moment mais cela n’a pas duré; c’était un sentiment qu’il n’avait pas vraiment. (There is an end to the feeling of being sorry and that end is situated in the past.)