Sir Alex Ferguson's side missed out on the knockout stages for the first time in six years after they finished third behind Basel and Benfica in the group stage.
A 3-1 loss to the Swiss champions then saw the 19-time English champions demoted to the second tier competition, the Europa League.
Phelan knows United need to avoid similar disappointment this season, where they will face Braga, Galatasaray and Cluj in the group stages.
"Europe's always big at this football club," Phelan told ManUtd.com. "The traditions are set within the European boundaries for Manchester United and we know we have to do better.
"We let Europe slip from our grasp too easily last year. The players are conscious and aware of that, although we haven't dwelled on it as that wouldn't be positive.
"We've put it down as a blip, but we know we have to do better."
Phelan has also called for the side to pull together and placed paramount importance on scoring more goals after a frustrating end to last year's league season.
Alongside their European disappointment, United missed out on claiming their 20th league title on goal difference to Manchester City in a final day thriller.
So far this season they have leaked five goals in their opening three Barclays Premier League games and Phelan concedes they cannot rely on "grinding out" narrow wins any more.
"You learn it's a team game, even though individuals change matches," Phelan said. "Everybody has to be fully focused for the entire match - from first to last whistle.
"I think we also know that we need to score plenty of goals. The old days of being able to win the league by grinding out 1-0 victories is gone.
"In this league now, every goal counts so we want to create more chances and score more goals.
"We also have to defend well as a unit. All those elements are very important."