Appleton, who is now unbeaten in six games since succeeding Holloway at Bloomfield Road, saw his second-half substitute pay dividends as Dicko forced the ball in from Wes Thomas' cross.
Nathan Delfouneso had given Blackpool a first-half lead but goals from Glenn Murray and Owen Garvan had appeared to set Palace on course for victory.
Appleton said: "I'm sure some players get themselves up for different games, former managers or clubs, and I thought we dealt with them reasonably well.
"I would have been desperately disappointed not to take anything out of the game after having played so well in the first half.
"I knew they would improve in the second half and it was difficult for 10 or 15 minutes in the second half.
"But just before we got an equaliser, you could see a bit of momentum building. And once we got that, I thought we could have gone on and got the winner."