The 34-year-old was adjudged to have fouled Ashley Young, despite replays showing that the Manchester United winger was offside.
There was also strong suspicion that Young dived to win the penalty.
Lineker has said that the FA's refusal to rescind the red card "beggars belief".
"Shaun Derry red card stands," he wrote on Twitter. "Who makes these decisions at the FA? Have they any feeling for the game? Beggars belief at times."
Lineker scored 48 goals in 80 appearances for his country.