United travel to Aberdeen for their opener before games against Motherwell and champions Celtic in the subsequent seven days.
McNamara said: "It's just one of those things in football.
"We have no control over the fixtures and we have to play every team at some stage or another. But the bigger the game the better and we also have faith in our players.
"We want to try and do better than we did last season, when we finished fourth and got to the final of the Scottish Cup."
United face a team that have already played six competitive games in the Europa League.
The Dons have impressed so far, despite exiting the competition against Real Sociedad in midweek.
McNamara said: "Aberdeen are organised, hard-working and dangerous, so we know what to expect and it's down to us to show what we can do.
"I'm sure their fitness will be fine having been in Europe and I think they will be okay for Sunday, even after playing on Thursday night."
United will be without defender Sean Dillon, who has undergone an operation on his fractured cheekbone. Dillon is joined on the sidelines by Mark Wilson, who is recovering from a broken foot.
John Souttar is still out due to an ankle injury but Keith Watson should make it back from a calf injury.