Eddie Howe's men appeared to be on the rough end of a few decisions in the game and Alexis Sanchez was lucky to stay on the pitch after his lunge on Garry Arter.
The Cherries had what many saw as two clear-cut penalty decisions turned down and Francis says the handball one was difficult for the referee to see, but easy for the linesman who should have stepped in.
He told the Echo: "It's difficult for the referee, having seen it back I'm not sure he had a great view of it.
"But I know for a fact the linesman's got an excellent view, he's in line with it, he's standing there. That's when you need your linesman to help the referee out.
"If he had put his flag up the referee would have given it, it's as simple as that.
"It's tough for a referee to give two penalties at the Emirates. But if they are penalties you have to give them, that's what you expect from a referee."