It is not customary to use "Dirooz Shab", it is like to say "yesterday night". Usually Dirooz refers to last day, but for last night you should use "Dishab".

Dishab, man raftam concert. Ba doostanam be concert-e "Radiohead" raftim. Radiohead gorouhe morede alagheye man hast (you can also use "hastesh" and "ast" instead of "hast" in this sentence). Anha behtarin-and ("behtarin" means "the best". behtar can be used when you want to compare two or more things with together. Unha behtar-and means "they are better").

Musice anha besiyar zibast (Which is not a common sentense, in farsi, you can say "Anha besiyar ziba Music minavazand.)

So I would translate your english sentence this way:

Dishab, Mano doostam be concerte Radiohead raftim. Radiohead gorouhe morede alagheye mane, anha behtarin-and va Music ro besiyar ziba minavazand ("Minavazand = ejra mikonan")

Radiohead

Dirooz shab, man konsert ro raftam. Ba Doostonam, ma 'Radiohead" Didim. Radiohead goruhe musighi morede alaghe man hast! Anha Behtar-and. Anha muzik kheili khoshgele hastand.

Last night, I went to a concert. With my friend, we saw Radiohead. Radiohead is my favorite band! They are the best. Their music is very beautiful.

Radiohead

(dishab)Dirooz shab, (man ba dostam consert raftam )man konsert ro raftam. Ba Doostonam, ma 'Radiohead" Didim. Radiohead goruhe musighi morede alaghe man hast! (unha behtarin hastand)Anha Behtar-and. (mosighie unha kheili zibast) Anha muzik kheili khoshgele hastand.

Last night, I went to a concert. With my friend, we saw Radiohead. Radiohead is my favorite band! They are the best. Their music is very beautiful.

Radiohead

Dirooz shab, man be konsert ro raftam. Ba Doostonam, ma be 'Radiohead" Didim. Radiohead goruhe musighie morede alagheye man hast! Anha Behtarinand-and. Anha muzik Muzike anha kheili khoshgele delneshin hastand ast.

Last night, I went to a concert. With my friend, we saw Radiohead. Radiohead is my favorite band! They are the best. Their music is very beautiful.