It leaves the Terrors eight points adrift of Kilmarnock at the foot of the Scottish Premiership.
"You think we are running out of games?" manager Paatelainen insisted. "No chance. We have a good chance.
"We've got plenty of opportunities and plenty of chances to close that gap and that's our aim."
United had taken the lead through Henri Anier, but Marvin Johnson equalised just before half time and Louis Moult grabbed the second-half winner.
Paatelainen thought that referee Crawford Allan got it wrong in awarding a free-kick in the lead up to the equaliser after Ryan Dow challenged Morgaro Gomis.
"I've seen it on video and, in my opinion, Ryan Dow just goes for the ball, he wins the ball, it is a clean challenge, so I don't think it was a free kick," he told BBC Scotland.
"I thought the first half performance, before the goal, was good. I thought we were on the front foot.
"We scored a good goal - a great strike from Anier - and we looked comfortable.
"Then softness at defending a set piece came to the surface again and we paid the price."
Motherwell's victory took them above Dundee into sixth place, but manager Mark McGhee was more concerned about injuries picked up by midfielders Stephen Pearson and Keith Lasley, as well as right-back Josh Law.
"Stephen, we are a bit concerned that he has damaged his ribs and he's certainly struggling a bit," he said.
"Las has a real dull one is in there with quite a lot of discomfort. Josh Law is the same.
"We have won tonight, but it's been at a cost."
McGhee's priority was still avoiding relegation trouble rather than a top-six finish.
"We might be back out the top six tomorrow, but more importantly it puts three more points between us the team sitting second bottom," he added.
"In the first half, we were very fortunate to go in level. I thought we were really poor.
"We didn't work anywhere as hard as we have been and certainly we didn't work as hard as we did in the second half.
"But the fact is we did get the equaliser fortunately and it gave us the platform to sort out a few things at half time and work harder in the second half.
"We certainly did that. They put in a tremendous amount of work in the second half and, in the end, thoroughly deserved to win the game."
Mixu Paatelainen insists that his Dundee United side can still escape relegation despite a damaging 2-1 defeat away to Motherwell.