Trotters substitute Chris Eagles conjured the winning goal for Dougie Freedman's side in the final minute of stoppage time, and despite the loss, Appleton was encouraged by the Rovers' display.
"Obviously Bolton are on a good little run at the minute and sometimes you go on a purple patch like that and things go for you," he said.
"But I certainly believe that the harder you work the luckier you become.
"I think that if we continue to play with the commitment, the effort and the attitude that we showed.... it was certainly a performance that sums me up as a person as well as a manager.
"I need 11 players who enter the field of play wanting to put in the type of performance that they did tonight."