And Scunthorpe could count themselves unlucky not to be awarded a late penalty when home captain Steve Fletcher appeared to haul down Ian Baraclough.
But match referee Grant Hegley waved away protests from the Iron players.
Laws said: "We could have had a penalty at the end. Steve Fletcher has virtually hauled him [Baraclough] down but the referee was never going to give that and we knew that from the first minute of the game.
"On one hand I'm disappointed because we led for so much of the game. But on the other hand I'm pleased with the players because we came here with a game plan to stifle Bournemouth's play and they did that well.''
Bournemouth manager Sean O'Driscoll was disappointed with his side's display.
He said: "I thought we were a little disjointed to start with but as the game went on we got better.
"I'm disappointed because we dominated the game but failed to create any real chances.'"