The result sees Swansea remain 19th, three points behind 17th-placed Everton.
Wilfried Bony had a goal disallowed by referee Stuart Atwell, the Ivorian's fine strike was chalked off after Jordan Ayew was alleged to have committed a foul in the box.
This decision angered the Swansea players, who had to be dragged away from the referee on the stroke of half time.
Positive start began to fade
As Clement made five changes to his starting lineup and tried another new formation, there was optimism in the air at the Liberty Stadium. Fans were louder than they had been, as Hymns and Arias roared around the ground prior to kickoff.
However it was Marc Pugh with the first chance of the game, as Josh King swept past Roque Mesa before delivering a cross that the Englishman scuffed his shot into Lukasz Fabianski’s grateful arms.
That aforementioned optimism soon turned to frustration, as Swansea were allowed plenty of possession, but failed to penetrate Bournemouth’s defence.
A swift, promising counter-attack on the half an hour mark led to Renato Sanches completely misplacing his cross for Bony, which summed up the kind of day Clement’s side were in store for.
Sanches then sent a shot into the side netting, the man on loan from Bayern Munich didn’t have his greatest game ever but he does look like he can create chances. Something Swansea desperately need.
Swansea had 1.9 shots on target per game through 12 games this season, the worst of any Premier League club in the past nine seasons through 12 games. (via James Yorke)
The game’s controversial moment came just before half time, as Bony’s fine strike was disallowed for Ayew’s foul in the box.
The Swansea players were furious at the decision, and had to be dragged away from the referee as he ended the half on a sour note.
Bony was denied his first goal at Swansea since leaving the club for Manchester City, and a chance to lift the mood at the Liberty Stadium after a dreary opening 45 minutes.
Swans start bright
Swansea started the second half well, pressing high and winning the ball back in Bournemouth’s half twice to produce chances.
If Clement isn’t doing a lot else right this season, his team talks seem to be working, and that’s evidenced by the improved performance his players put in after the break.
However it was the Welsh side’s final ball that let them down time and time again. It’s to be expected really, when you sell your £45 million rated playmaker in the summer and decide against signing a replacement.
In August 2016, owner Steve Kaplan said: "We're not going to outspend many other clubs in the Premier League. We've got to be a little bit faster, a little bit smarter, a little bit craftier."
Swansea however did not act faster, smarter or craftier, and they are being punished for that this season.
The game then turned feisty after 75 minutes, as Martin Olsson and Jordon Ibe started pushing each other before Ki Sung-Yueng got involved. The three of them were all booked.
The game’s best chance then fell to substitute Leroy Fer, who drove past several Bournemouth players before firing his first shot at Asmir Begovic and clipping the crossbar on the rebound.
Swansea then had a penalty appeal turned down, as Tammy Abraham was alleged to have been clipped inside the area but the referee turned it away.
Bournemouth had a late chance to nick it, but no one could get on the end of Charlie Daniels' teasing cross to turn it home.
However it’s yet another game where Swansea have failed to score. They need to start picking up wins, and won’t do that without getting on the scoresheet.
This was meant to be a winnable game, and it was. With the festive period heating up soon, Swansea need to start picking up three points instead of just one.