Ferguson was clearly being held back by the Costa Rican, but the referee, Steve Dunn, failed to give a penalty. However, he then showed Ferguson the red card after Wanchope crashed to the floor and writhed around in apparent agony.
To rub salt into Everton's wounds, Wanchope scored Derby's second goal as the Rams won 2-1 for only their third away victory of the season.
Kendall said: "I don't need to see it again. It was very clear that Duncan was pulled back in the area and he reacted to that. As far as I am concerned a penalty should have been given - and then Duncan sent off." Kendall refused to say what action, if any, will be taken against Ferguson.
Everton had a torrid first half, with Mickael Madar and Tony Grant limping off. Five minutes after Ferguson's dismissal, and with Everton still trying to reshape their side, Igor Stimac headed Gary Rowett's corner through goalkeeper Thomas Myhre's hands for his first goal of the season.
Derby moved closer to victory five minutes after the interval, when Wanchope tapped the ball home from close range after a four-man move had cut the Everton defence apart.
An overhead kick from Claus Thomsen brought him his first goal for Everton and gave them late hope of snatching a draw, but Derby were able to hang on.
Goals: Stimac ( 21) 0-1; Wanchope (50) 0-2; Thomsen (85) 1-2.
Everton (4-4-2): Myhre; Thomas, Short (Bilic, 81), Watson, Tiler; Ball, Farrelly, Grant (Thomsen, 38), Oster; Madar (Cadamarteri, 14), Ferguson. Substitutes not used: Allen, Gerrard (gk).
Derby County (4-4-2): Poom; Rowett, C Powell, Stimac, Sturridge; Wanchope, Delap, Willems (D Powell 72), Carsley; Eranio, Dailly. Substitutes not used: Bridge-Wilkinson, Elliot, Kozluk, Hoult (gk).
Referee: S Dunn (Bristol).
Bookings: Derby D Powell, Eranio, Stimac. Sent off: Everton Ferguson.
Man of the match: Stimac.