A superbly taken finish by Hornets skipper Troy Deeney condemned the Toffees to a defeat in what was a dreadful game.
Neither side particularly controlled the Premier League match, with Everton offering nothing to the contest.
And Allardyce has placed the blame firmly at the feet of his players.
He said: “It’s their responsibility at the end of the day to do better isn’t it?
“They’ve had the opportunity to deliver away from home and they haven’t done it again.
“It was a very similar team to the one that comfortably beat Crystal Palace 3-1 at home two weeks ago
“They created opportunities, failed to take them and at the end of the day we’re in a results business so they should have said ‘Right it’s not going our way lads, so let’s make sure we don’t give one away’”.
Everton have won just one of their last 22 Premier League games away from home, and have not kept a clean sheet since Boxing Day.
They face a crucial trip to Turf Moor to take on Burnley, with Allardyce wanting more from his players.
“We have to do better and make sure we try and do better next week,” he admitted.
“Whether I change the side and move that side around depends on who’s available and what sort of week we have.
“We certainly have got to turn away results into more positive ones and we need to do that quickly because we heap too much pressure on ourselves at home.”