United entertain champions Celtic on Saturday, live on Sky Sports 3 at 12.30pm, and McNamara's men go into the match six points behind Aberdeen and Motherwell.
The Tannadice club end their campaign at Celtic Park, but still have home games against both their rivals for second place.
"I think it's still there for us," McNamara said. "It's obviously a big ask. Aberdeen and Motherwell are going very strongly, but obviously we've got a massive game for us against Celtic, so we'll go and do our best.
"We're chasing them at the moment and we have been for long spells in the season. Great credit to Motherwell and Aberdeen for the consistency they have shown over the season.
"But again Celtic have been so dominant this year in the league, so a hard game for us on Saturday, but it's one we look forward to."
United are still chasing a European place on two fronts this season, and after the home match with Celtic they play League One Rangers in the Scottish Cup semi-final at Ibrox the following week.
While important fixtures are coming fast for his young team, McNamara is heartened by United's recent run which has resulted in just one loss in 11 games.
McNamara added: "Naturally the cup game, the one-off game to get to the final, is a massive incentive for us at Ibrox, but we'll focus on Saturday first and try to get the three points at home then we'll turn our attentions for a big week building up for the Rangers game which looks like a massive one for both teams.
"Rangers have had a good season as well. They've won their league comfortably. They have a Ramsdens Cup final this weekend to look forward to so it should be an entertaining game next week.
"We're on a decent run. We had a decent run before Christmas. We had a bad spell over the Christmas period, we hadn't won in six, since then we seemed to have turned a corner and a good spell at the moment.
"We're all hopeful that we can keep it going until the end of the season. We're coming into form at the right moment."