United just scraped into the top half of the table ahead of the split last term before finishing in sixth spot.
And McNamara, who took over as boss at Tannadice in January, wants to ensure the club is moving forward under his stewardship as they prepare to kick off the new campaign at Partick Thistle tomorrow night.
He said: "First and foremost for me, I want to progress from last season.
"As a club, I thought we underachieved, especially at home. Our home results were very poor for the fan base we've got.
"Top six is a minimum for us. I want to take the club forward and try to be successful here."
As well as champions Celtic, St Johnstone and Motherwell are also flying the flag for Scottish football on the European stage, while Hibernian have already crashed out of the Europa League in embarrassing fashion.
McNamara believes Europe should be an aim for United next year but admits his own side may have struggled on the continental stage this time.
He said: "If we had got into Europe last season, I don't think we would have been ready at the start there.
"It was important that we had pre-season behind us, with myself and new players coming in.
"But hopefully, next season, it's something we can build to."
The pre-season campaign yielded a morale boosting win at Wigan in a friendly last Saturday, as United prepare for the action to begin for real.
McNamara said: "The good thing from the Wigan game was a clean sheet from a defensive point of view against a very good side.
"The lads go into this game full of confidence, not just because of the results but also the way we played in spells in the last couple of games."
McNamara departed Partick in what proved to be acrimonious circumstances, before both clubs finally agreed on a financial settlement in June.
And he was not surprised to see himself up against Alan Archibald's side in the SPFL curtain raiser after the Glasgow club sealed their place in the top flight.
He said: "As soon as the promotion was sorted, I think everybody knew that was going to be the case.
"It's a funny old computer that does the fixtures.
"We've got to face them at least three times this season so we will go down there and hopefully get the three points.
"Archie has added a couple of players but essentially the majority of the players are the ones we worked with last season.
"They have a lot of good young players, who are hungry and have a lot of ability.
"It should be a good game, with both teams trying to play football. Hopefully we will be victorious."
On his return to Firhill, McNamara added: "I think it will be quite hostile, just with the way things have happened.
"I wouldn't change anything. I will just go there and be professional and try to get the three points for my new club."