Swansea manager Steve Cooper lamented his side's poor defending after their automatic promotion hopes suffered a setback following a 3-0 defeat at Bournemouth.
Cooper said: "It has been a very busy period and we might have been a bit fatigued.
"But I am not going to use that as an excuse. The first two goals were so unlike us and what we pride ourselves on. They were really poor goals to give away.
"The first one was a cross into the box where we were not marking and the second one is the first contact off a corner.
"We gave ourselves what ended up being too much to do. Our general play was okay but I thought we could have been better in the final third.
"We did not back ourselves enough and did not commit enough in the final third. It was a frustrating night."
Billing had already seen a shot blocked when he opened the scoring in sensational fashion in the ninth minute.
Holland midfielder Danjuma raced away down the left wing before cutting the cross back for the unmarked Billing to plant a stunning left-foot volley into the net.
Bournemouth doubled their lead in first-half stoppage time when Danjuma's corner hit Latibeaudiere on the back, sending the ball spinning into his own net.
It would have been game over 10 minutes into the second half but for a good save from Swansea goalkeeper Freddie Woodman.
Danjuma whipped in a teasing free-kick which was met by a powerful header from Cameron Carter-Vickers but Woodman managed to claw the ball over the crossbar for a corner.
Begovic was called into action again 10 minutes later when he reacted smartly to keep out the lively Whittaker's low shot from a Ryan Manning cross.
Danjuma sealed the points three minutes from time with a thunderous left-foot drive into the top corner after Billing had deftly laid the ball into his path.
The win was a welcome confidence boost for Bournemouth ahead of Saturday's FA Cup quarter-final clash at home to south coast neighbours Southampton.
Woodgate said: "Every single player did well. Jack Wilshere basically ran the game for the 70 minutes he was on.
"I thought his was an outstanding performance and he gave us something we have not had in the last few games.
"They are a really good team and we did well. I thought we dominated."
On Billing's goal, Woodgate added: "Billing owed us one because his performance against Barnsley when he came on was not great.
"Hopefully he can push forward now and get in the Denmark squad for the Euros. That is his aim for the season and he is a player of exceptional quality."