Silva was taken off on a stretcher after being caught by Kouyate in the 67th minute of West Ham's 2-0 defeat to City on Sunday and receiving several minutes of treatment.
Kouyate was booked for the incident, with City boss Pellegrini since confirming that Silva has been taken to hospital.
But Allardyce said: "It's accidental, it looked pretty innocuous to me I didn't even think it was a foul. I've just had a look now, it doesn't look deliberate at all to me.
"He [Kouyate] has no idea because it's happened from behind him, he doesn't even think that he's done anything."
The points had been all-but settled by the time Silva went off. An 18th-minute James Collins own goal giving City the lead, which was doubled by Sergio Aguero after Stewart Downing lost the ball in midfield.
Asked about his side's performance, Allardyce added: "I think the disappointing thing in the first half was the goals were gifted to Manchester City and the second thing was the amount of possession we allowed ourselves to lose.
"The two mistakes we made for the goal - one was pretty bizarre and the other one was unexpected from a player as experienced as Stewart Downing.
"Second half, eventually changing the system got us back to playing better going forward and when we create two chances as good as Enner Valencia's and Kevin Nolan's then we've got to convert them."
