Two of Everton's three goals came from set-pieces as Louis Saha and Joseph Yobo punished Blackburn for slack marking on a free-kick and corner respectively.
Saha also grabbed a goal from open play to complete Allardyce's misery and he was eager to vent his anger at his side for failing to comply with his training ground methods.
"We're very disappointed with the nature of the defeat and the way in which we conceded the goals," he told Sky Sports.
"I think we've gifted Everton the three points today rather than Everton being on blistering, top form and they've taken full advantage of the gifts we've given them.
"Two set-pieces - a corner and a free-kick. We've spent an awful long time on making sure we didn't concede goals in that way and we have done, and that's what's cost us the game.
"We're hugely disappointed with that and we've got to put that right for when we play on Tuesday night at (Nottingham) Forest in the Carling Cup."
Relegation ZoneBlackburn now slip into the relegation zone as Everton's win takes them up to 13th in the Premier League table.
The defeat is a heavy blow for Allardyce to take after his side appeared to have their season up and running following last weekend's 4-0 win over Wolves, their first win of the season.
The former Bolton boss now admits that he may be forced to drop players after the Goodison Park showing and has vowed to make full use of his squad.
He said: "I think that we've got a squad that we need to use.
"We need to find the players to come in and take the opportunity to show us what they can do because certainly, a lot of the players today played because of such a good performance against Wolves.
"And today they've put their places in jeopardy, so the rest of the squad will be looking on and saying 'I've got an opportunity now and if I do get it let's grab it.'"