The Paisley club head into the weekend action in 10th position, level on points with top-flight newcomers Ross County, and the defender admits they should be enjoying a loftier place in the table.
However, Barron hopes positive results against Dundee United and Kilmarnock in their next two games will give their SPL standing a much-needed boost ahead of next month's winter break.
He said: "Everyone here feels we should be a bit higher up the table. But the table doesn't lie and we know that.
"We will just look to put that right in the second half of the season and try to push for that top six spot, where we feel we should be.
"We will hopefully try to push on up the table now.
"It's a really tight league so if you can put two or three wins together, it can shoot you right up the table. We will be looking to do that.
"We will be looking for two positive results before the break so that we can head into the winter break knowing we are in a comfortable position."
Saints travel to Tannadice on Sunday and Barron wants three points against a United side he fully expects to put an impressive run together in the latter stages of the campaign.
He said: "It's another away game so any result would be positive for us, although I'm sure we will be looking to get all three points.
"Their form has been a little bit indifferent this season but they always tend to do well towards the end of the season.
"Hopefully they can wait until after New Year before they start doing well.
"We will be looking after ourselves and trying to get the win."
According to Barron, confidence is high in the Buddies camp following a win and a draw against high-fliers Motherwell and Inverness respectively.
He added: "If someone had told us we would get four points from those two games against Motherwell and Inverness, we would have taken it.
"Both of those teams are flying just now.
"To go up to Inverness and get a point against the team sitting second in the league was a positive result for us."