Marc Pugh's strike sealed the Cherries' fully-deserved 1-0 win over reigning champions Leicester City at Dean Court on Tuesday night.
Howe hailed Bournemouth's rapid six-year drive from League Two to the Premier League's top half, but admitted he remains hungry for more.
"We're building nicely; the team is growing and getting better and there's still a lot more to come," said Howe.
"We're in a really good position to hopefully kick on and get better further.
"I think it's an understatement really, from our perspective, to be happy.
"The club's come so far so quickly, sometimes it's maybe nice for others to sit back and enjoy the position we're in.
"But for me I'm always looking for more and to achieve the next goal, and that's to try to beat Southampton."
Bournemouth host local rivals Southampton at Dean Court on Sunday, with Howe far more concerned with how to topple the Saints than lingering on any idle thoughts of continental qualification.
"I'm not going to say Europe, I'm going to say I want to make the team better; I want to make the team stronger," said Howe.
"And in many aspects I believe that's possible
So what that leads to, who knows.
"But when you consider where the club was a few years ago you wouldn't have thought this was possible.
"But it's not my job to sit back and look at that achievement in any kind of way, because there's another dream to chase now."
Leicester now boast the unwanted record of the worst return from their first eight away league matches for any reigning Premier League champions.
The Foxes have just one point from their eight encounters on the road, leaving boss Claudio Ranieri at a loss to explain that paltry return.
"I think the result is too harsh for us, we deserved a draw," said Ranieri.
"I know we only have one point from eight matches away from home.
"But I think we can improve, because I'm sure in the next eight matches we'll do something more.
"Look, in the Champions League we've played well (away from home)
In the Premier League; no
Why? I don't know.
"We have to react, we have to concentrate more, to be more determined.
"We need more will, more desire, more everything."
Source : PA