Saints were unbeaten in four games over the festive season which took them 13 points clear of the struggling Taysiders in 10th place, albeit having played a game more.
However, ahead of the visit of second-bottom Ross County, the former Derby and Sheffield Wednesday winger does not consider the Dees to be a safety net.
"We don't think that Dundee are cast adrift," said the 34-year-old. "People said that earlier on in the season and then we went on a run where we didn't win for six games.
"They caught up with us and when we played them they could have gone above us, so it shows how easily it is done.
"The results we had in October and November, they were terrible , there is no getting away from that.
"But we are a positive thinking club and with the results we had after that run we were on, we have kicked on.
"Our aspirations are top six. The league is so tight that two results will probably put us up and to where we think we should be in the league."