Posh got in front after 10 minutes, Gayle sweeping home after Jake Kean made a fine double save from Danny Swanson, and it was 2-0 a minute later when Gayle headed in Bradley Orr's cross.
They hit their shellshocked opponents again after 27 minutes, Gayle following up a Kean save from Lee Tomlin's low effort to expertly dummy and slam into the open goal to complete his treble.
"He's a very good player. He's better than I thought he would be," Ferguson said.
"He's technical, doesn't give the ball away and makes clever runs. He's the real deal. There's no question about that.
"He will score goals. He's a goalscorer. I thought him and (Nathaniel) Mendez (-Laing) were a real threat."
Ferguson lauded all of his players after a first-half display that left them out of sight.
He said: "I don't know if we should have been hanging on as it doesn't justify our performance in the first half, which was outstanding. To come here and be 3-0 up, and it could have been more. I thought my players were outstanding."
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- Jake Kean