An own goal from Alfie Mawson and a Benik Afobe strike either side of half time saw the Swans fall to successive league defeats for the first time under Clement, leaving them 17th in the Premier League table.
Swansea do still have a three-point cushion to the relegation zone, but Clement believes that his side now need to win their next two home games - against fellow strugglers Middlesbrough and high-flying Tottenham Hotspur.
"Clearly it wasn't good enough on the day. For periods going into their first goal we did okay. We have to rebuild and go again because Bournemouth have showed, they were right in it and they've just won back-to-back games at home and that's what we have to do now," he told BT Sport.
"We go and play two home games, Middlesbrough, a massive one in two weeks' time, followed by Tottenham, which is obviously a difficult one. We have to remember that we've come a long way in a short time.
"[There are] nine games to go and I've still got a lot of belief that we can (stay up). Our objective is to come 17th or higher. I have to say congratulations to Bournemouth, they deserved to win. We're going to fight hard to the very end and I'm sure it will go to the very end."
Swansea have now won five and lost five of their 10 Premier League games under Clement.