Francis is backing his team to deliver results, despite his concerns over injuries picked up by Junior Stanislas and Benik Afobe during the 1-0 defeat by Chelsea on Saturday.
"The Chelsea game was not going to make or break our season but the next three, four or five games certainly will so we have to put in maximum performances to try to get maximum points out of them," Francis told the Daily Echo.
"We haven't had a start like this in the Premier League. If you look back over the past couple of seasons, we were higher than we are now.
"But we have had dips in the season before and have bounced back. I've always said how good the character is so I'm not too worried about that side of things."
Bournemouth have seven points from 10 games, five fewer than at this stage last season and one less than in their inaugural Premier League campaign.
However, five of the seven league defeats have been by a single goal.
"I can certainly look back at games and feel we were hard done by, where we should have won or picked up a draw. But at the same time you can't dwell on that," Francis added.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
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