After Ryan Mason cancelled out a Charlie Daniels strike, Eddie Howe’s side stepped it up a gear with Steve Cook, Callum Wilson, Dan Gosling and a double from Junior Stanislas ensuring the three points remained at Vitality Stadium.
Francis believes that the Cherries were worthy of their victory and spoke of the notable team spirit within the squad.
"It’s probably easy to stand here now and say that it’s been coming for a couple of weeks," Francis said.
"We’ve created chances and been outstanding in and around the opponent’s box, but things hadn’t quite fallen for us. It’s nice for everything to come together today.
"I thought we were well worth our goals. The manager has done so well, especially in the transfer window. He’s brought in players that can attack, create goals and score goals and it certainly looked like that today.
"Hopefully that can continue and we can keep putting chances away in front of goal. It’s been a great team spirit and the manager builds that and when we score goals he wants everyone celebrating together.
"It’s a team game out there. It’s great to get the win but more importantly we played well as a team and everyone did their jobs."
The Cherries captain also looked ahead to next week’s visit of Tottenham Hotspur and how his side can right the wrongs from the two defeats suffered to Mauricio Pochettino’s men last season.
"I think it’s going to be an excellent game," Francis continued.
"Hopefully we can get our own back. We had two disappointing defeats to them last season and we weren’t anywhere near their level nor anywhere near our level.
"We’ve been excellent at home of late so we’re hoping that form can continue going into the game."
