Blackpool, who have yet to win under Appleton, looked set for an afternoon of disappointment as they fell 2-0 down after just 21 minutes following goals from Ikechi Anya and Troy Deeney.
But veteran striker Kevin Phillips pulled one back for the hosts just after half-time before Isaiah Osbourne struck a stoppage-time equaliser to make it 2-2.
Appleton felt they created enough chances to win the game.
He said: "We didn't do enough in the first half and maybe we switched off for both of Watford's goals.
"In the second half I thought we looked comfortable and created enough chances to have won the game.
"I think we restricted Watford to having just three scoring opportunities throughout but despite that we have still only managed to get a point."
On what was said to his players at the break, Appleton added: "I said a lot at half-time but it wasn't a situation where I was ranting and raving.
"We changed the system a little bit to allow the full-backs to get a bit higher up the pitch, which allowed our wide players to support the front men better."