The England lock insists he and his team-mates want more, targeting a top-two spot after four successive wins.
Saints defeated Exeter Chiefs 13-12 at Sandy Park last weekend, moving into the Gallagher Premiership play-off places as a result.
And Ribbans said: "We've had a good couple of results recently and the confidence is slowly coming back into the squad, which is really good, but we're not happy with fourth.
"We definitely want to be a lot higher in the table - we want to be first or second and we believe that we can be.
"We haven't taken our win at Exeter for granted, we're still working really hard and we're looking for another big performance this weekend against Bath."
Ribbans has been one of the stars of the season for Saints.
And when asked about his own form, he said: "It's going alright, I've been putting in some good shifts for Saints and that's all I've really been focusing on.
"I know what Boydy (Saints boss Chris Boyd) and the coaches want from me as a player and I'm just trying to do my bit."
Saints have not played a home game since beating Worcester on Boxing Day.
And they can't wait to be back at Franklin's Gardens for this afternoon's fixture against Bath (kick-off 1pm).
"I'm tired of bus trips and hotels away and we're really looking forward to being at home," RIbbans said.
"It's going to be similar to Exeter in terms of the way Bath play. They're a physical pack trying to be dominant and it's going to be another massive effort from the forwards this weekend.
"Hopefully we can also put some of the Saints flair that everyone likes to see on them, but it's definitely going to start up front and we're going to have to win that physical battle again."