Junior Stanislas fired the winner in the 23rd minute with a fine 20-yard drive, as Bournemouth held firm for their second clean sheet and victory of the Premier League campaign.
Howe firmly believes Bournemouth can better last term's Premier League debut finish of 16th, but challenged the Cherries to prove his convictions correct.
"I said previously I believe we are better than last year but that can look foolish if we don't back that up," said Howe.
"That has to be decided on the pitch, that has to be proved week in week out.
"On paper is a dangerous thing, I would believe so but we have to prove that.
"It's difficult to say that now, we have to prove that at the end of the season."