The Spanish striker was on the scoresheet as the Serie A champions downed Milan 3-1 at Juventus Stadium on Saturday.
It was the fourth time in the past six games that Morata was handed a start, as Allegri continues to decide on who is the best partner for regular starter Carlos Tevez.
But, while giving credit to the blossoming partnership between Tevez and Morata, Allegri was keen to highlight the strength of his striking options.
Asked whether Morata had done enough to cement a starting place, he said: "Well I have got five strikers at my disposal and they are all quality strikers and that’s important."
"It's normal that the more the players play together the more they know each other, so Morata and Tevez are playing more and more together and it's normal that they can only improve."
Allegri also stated that sought-after midfielder Paul Pogba will continue to improve after falling below his usual level for the league leaders against Filippo Inzaghi's men.
"Pogba is young and he is a fantastic guy who still has space for improvement," he added.
"It's normal that he must grow up especially because he needs to understand the moments when he can do certain things and there are other moments when he can't."
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