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 Saturday's 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."
Teale enjoyed his first winter break but admits it may have been beneficial if the Buddies had kept their momentum going.
He said: "It was nice to get that time off. It was something I hadn't experienced in my career."
"I was in Dubai for a few days with my wife and kids, it was great.
"But from a footballing side of things, we would probably have carried on because we did have a few decent results and confidence was high."
"We hope we can carry it on tomorrow but time will tell."
St Mirren boss Danny Lennon is hoping a pricing initiative will help swell the gate for the lunchtime kick-off in Paisley.
He said: "Our club has reduced admission to £10 and £5 concession and under-12s get in free."
"So it is fantastic and a thank you for the support over the festive season and also when finances are tight in January following Christmas."
"Hopefully we get a great turnout. It is important that we encourage fans back in."
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