Boro were cruising after first-half goals from Ishmael Miller and Richard Smallwood but Blackpool hit back in a ding-dong second half, clawing one back through Wes Thomas before Scott McDonald restored Boro's lead.
Blackpool forced a second through Chris Basham then in a pivotal moment won a disputed penalty only for Jason Steele to save superbly from Thomas Ince. Boro sealed it late on through Adam Reach.
Appleton said: "It was disappointing for myself and the staff and more so for the players because they were well short of how they can play.
"I've got to say I didn't see that first half coming. We improved in the second half and nearly did enough to get back into it.
"At the end of the day we are one excellent penalty save away from salvaging a game away at a side that are up at the top.
"When I took over people told me when Blackpool are good - very, very good - but when they are bad they are awful. I think in the first half I saw that bad side."