However, Allardyce, who succeeded Roy Hodgson as manager after England's underwhelming Euro 2016 campaign, said there was still time for Barkley to feature in his future plans.
"We have had to make a few difficult decisions and none more so than Ross Barkley," Allardyce told reporters on Monday.
"For him it's disappointing, for me, you have to make these decisions. The door will always be open for Ross but right now I feel the squad I've picked is the right one."
Marcus Rashford also missed out, instead selected for the under-21 squad against Norway, even though the 18-year-old striker featured for England at Euro 2016 and scored Manchester United's injury-time winner against Hull City on Saturday.
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"Having international experience in the under-21s will prove invaluable for us further down the line," the former West Ham, Bolton Wanderers and Sunderland manager added.
"If he plays for Manchester United on a regular basis, if he is regularly breaking into the United team then it will be a good basis for inclusion in my squad."
Allardyce, 61, will take his first training session with the players later on Monday with several, most notably Manchester City's goalkeeper Joe Hart, involved in speculation over their club futures ahead of Wednesday's transfer deadline day.
"If Joe arrives today, and I'm sure if there's anything in the pipeline Joe will tell us this may happen. Then we can get ready if it does," Allardyce said.
Slovakia held England to a goalless draw in their last meeting little at Euro 2016, a game Allardyce expects will have little bearing on Sunday's meeting in Trnava.
"The tactics will be different when we play them in Slovakia. That team will have to come out to attack us, they're playing at home, whereas in the Euros, we knew that one point was enough for them.
"They were a very sound, solid unit that proved very hard to break down, because they weren't interested in playing any type of attacking football I don't think."
(Reporting by Neil Robinson; Editing by John O'Brien)
