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But he stressed Saturday's results had not increased the game's significance.
United drew 0-0 at Hamilton Accies as the hosts missed a late penalty, while Kilmarnock moved above Motherwell by beating them 2-0.
"Nothing changes there. Every one of our matches is massive," Paatelainen told BBC Scotland.
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United now trail Motherwell by 12 points, with a game in hand, with Kilmarnock one point better off.
While the Tannadice side have now lost just once in five games, Paatelainen says it is not only games against other teams scrapping to avoid survival that they have to win.
"I think we need to win more than that," he added.
"I think we're well capable of doing that. The determination and quality are there in the squad.
"What we need and want to do is win every game, whether it's against a team directly above us or up the table."
Their recent improved run of results gives Paatelainen heart they can still turn their season around from a parlous position.
"That sounds better than the runs we've had," he continued. "Prior to this match it was three wins in the last four games and now a clean sheet, pick up a point.
"I thought three points would have been what we deserved.
"A few weeks ago we would've lost that game. Now we didn't and it could be a very important point at the end of the day.
"We want to make sure we are ready on Tuesday and do our best."
The goalless draw keeps Hamilton 15 points clear of United, but they are in a group of five teams separated by only three points, none of whom can be certain of avoiding a relegation play-off.
"There'll be lots more twists and turns because there's so little between the teams," Accies manager Martin Canning told BBC Scotland.
"One thing either way can win or lose you a game," added Canning, who watched as Ali Crawford's terrible spot-kick was saved.
"Kilmarnock - on the back of losing two big games against United and ourselves - have gone and beaten Motherwell. That just sums the league up.
"We just need to take care of our own business but that's four clean sheets in our last five, which is a big positive."
Dundee United manager Mixu Paatelainen acknowledges Tuesday's bottom-of-the-table clash with Motherwell is of great importance.