Sky Blues' fans staged an angry demonstration following Everton's victory, chanting for Strachan's head - the first time he has had to suffer such an indignity since taking over in November 1996.

Strachan insisted quitting has never entered his mind, despite whispers to the contrary, but admitted he and his players were "devastated and embarrassed" by their display.

But the manager refused to speak about the "Strachan out" chants, nor a confrontation with an angry fan near the tunnel, and the mood in the Coventry camp was summed up by midfielder Lee Carsley.

He said: "The fans are paying their money and if they have paid their money, they are entitled to have their say.

"Everton are a poor team and were there for the taking. Afterwards, the manager just said we have got to have a good look at ourselves, and no one has come out of the game with any credit.

"We were proved second-best. We let the manager down, everyone in the squad did, we were just not good enough."

But Carsley was insistent that the Sky Blues will start next season in the top flight, for the 35th consecutive year.

"We definitely will. We have enough quality in the club, it's just a matter of the players needing to start performing to the best of their abilities."

In the first 45 minutes, Coventry were shocking, while Everton made light of their injury crisis to ram in three goals before half-time.

Scot Gemmill inflicted the first wound, seizing on Danny Cadamarteri's astute pass to finish superbly.

Cadamarteri himself scored the second after the move of the match. Four players were involved in a breakaway before Niclas Alexandersson's cross was brought down by Cadamarteri, who slipped the ball under Chris Kirkland.

Kevin Campbell, Everton's skipper for the day, capped an excellent afternoon with the third, following some neat skill and forceful running by substitute Phil Jevons.

Strachan was blunt in his assessment, saying: "The whole thing was an embarrassment to ourselves and to the club.

"That includes myself, the squad, the coaching staff and even the players who were not playing. If they are not good enough to get picked for that they really must be embarrassed."

The Sky Blues did pick up in the second half, and Carsley scored a penalty with five minutes remaining after being tripped by keeper Thomas Myhre.

But Strachan could take no solace from anything, admitting: "It's something that will stick in our memories for a long time and we will have to put up with that."