Aberdeen have the chance to move up to fourth with a win over Craig Levein's men at Pittodrie this weekend.
But Calderwood admits a loss would leave his players with a massive task to catch Hearts and United.
"It is imperative that we take points in every match as the games are running out," he said.
"If we were to lose on Saturday and Hearts won, then we would be seven points behind them and five behind United.
"In the past, we have been 11 points behind teams and caught them but you want to avoid getting yourself into situations like that if you can help it."
But the Dons manager stressed defeat on Saturday would not leave his side completely out of the running to finish best of the rest behind the Old Firm.
He added: "As Craig Levein has already said, a defeat in this game would not be the end of the world. Our chances of finishing third would not be completely gone but it would make life very, very difficult.
"At the moment, we just have to focus on clearing the hurdle of getting into the top six and then if we achieve that, we can aim for third.
"However, there is no doubt that if we got three points this weekend, it would be a big help for us nearer the end of the season."
Calderwood believes United's recent dip in form has been due to Scott Robertson's absence through injury as well as the recent departure of Willo Flood to Celtic.
He said: "Craig Levein has been very unlucky having Scott Robertson out because he is a player that has been wonderful for him.
"Willo Flood was another important player for United that they no longer have.
"I know how Craig must feel because we have missed Jamie Smith all season who is a massive player for us. But we know they will still be a very difficult team to beat."
The Dons will be out for revenge having lost their two previous meetings against their New Firm rivals this season.
"I thought we were unlucky both times we played United," said Calderwood.
"We dominated the match at Pittodrie but couldn't break them down. At Tannadice, it was a couple of stupid mistakes that cost us.
"The two teams are very well matched and I am anticipating another close game this weekend.
"Dundee United have set very high standards for themselves and they are a very difficult team to break down.
But I think we have been unlucky against them this season so hopefully it will be our turn this time."
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