Allardyce let down by 'sloppy' Everton
The result saw Everton suffer their first loss since Allardyce took charge, while Bournemouth lifted themselves out of the bottom three and ended a run of eight Premier League games without a win.
Ryan Fraser – who had opened the scoring – netted the 89th minute strike via a deflection off Phil Jagielka to snatch all three points, but Allardyce felt Everton gave their opponents a helping hand.
"We gifted them the goals with sloppy possession," Allardyce told Sky Sports. "We have been the victim of our own errors which is disappointing. We must eliminate those simple errors.
"When we did play in the right areas we could have created more. Overall it is disappointing – it was a great run which has come to an end.
"The squad is trying to get fitter. We have players coming back from injury, so it's a bit of a struggle at the moment. We will persevere."
Relief was the overriding emotion in the Bournemouth camp, with boss Eddie Howe overjoyed at luck finally shining on his men.
what an effort! Fraser's brace seals a dramatic victory over @Everton ! #BOUEVE | #afcb pic.twitter.com/PWa9LR3ajL
— AFC Bournemouth (@afcbournemouth) December 30, 2017
"[It is] a massive win," Howe told BBC Sport. "We got our reward finally after a tough fixture list.
"We should have beaten West Ham and didn't, but we kept on going. Ryan Fraser has been excellent in recent weeks and he deserved the two goals.
"You don't want to be in the bottom three for a second, we've had to deal with that but we're out now.
"Runs of results can make a massive difference to a season – it's so tight in this league."