Rovers' hopes of a late surge towards the play-offs are fading after a fourth game without a win as headed goals from Chris Wood, Harry Kane and Andy King reignited Leicester's automatic promotion challenge.
Appleton saluted Schmeichel's save midway through the first half and was left wondering what might have been had Morton Gamst Pedersen's volley gone in.
He said: "We were beaten by the better side, but who knows what might have happened had we not witnessed a world-class save.
"If you get the first goal things can turn in your favour, but they got the first goal and went from strength to strength.
"The goals we conceded were a big disappointment for me, it was unlike our players. But it is hard for me to be too critical of the back four because they have been magnificent while I have been at the club.
"We move on now and I will be looking for a reaction on Saturday."