United opens its campaign at home to Galatarsaray on Wednesday and also has Braga and Cluj in what should be a comfortable group for the three-time champions.
But last year, FC Basel and Benfica finished ahead of United in one of the biggest shocks in the Champions League.
"If we don't go through, we will be criticized and pilloried for it and quite rightly," United manager Alex Ferguson said. "We've had our warning and I don't anticipate going out this time.
"Certainly, we'll do better than last year — no question about that."
United has a memorable history with Galatasaray, with fans of the Turkish club greeting their English counterparts with the banner "Welcome to Hell" when Ferguson's side visited Istanbul for a European match in 1993.
"I remember it vividly. It's one of those memories that will always stick with you," United midfielder Ryan Giggs said. "There were things thrown at us when we were driving away on the coach, fans outside the hotel chanting all night making sure we didn't get any sleep and people phoning the hotel rooms. It had everything."
Galatasaray should be the one having an uncomfortable night on Wednesday.
United has won its last three matches in the Premier League to climb to second place behind Chelsea, while new striker Robin van Persie will be refreshed about being rested for the 4-0 win against Wigan on Saturday.
Wayne Rooney is still out with a gashed leg but with Danny Welbeck and Javier Hernandez, Van Persie — a scorer of four goals in four league appearances for United — isn't short of strike partners.
With captain and defender Nemanja Vidic back, United has a squad capable of going all the way and improving what Ferguson often says is an unsatisfactory number of titles in the European Cup or Champions League for such a big club.
"We've had opportunities in the competition," Ferguson said. "We've lost two finals to Barcelona and won two in the last decade or so but we want to do better.
"The European Cup is incredible . it elevates your status within the game like the Real Madrids and AC Milans. We want to be up there in terms of the number of trophies won in European football."
Galatasaray is back in the Champions League for the first time in six years and is top of the Turkish league having won three of its four matches, most recently a 4-0 victory at Antalyaspor on Saturday.
"We have gained morale for the Manchester (United) game," Galatasaray coach Fatih Terim said. "Our supporters are expecting good results from the team. We want to make a good start by finishing with a respectable result in Manchester. We want to make it out of that group."
Although it was a 2-1 loss at FC Basel in the final group game that ultimately cost United last season, it was the sloppy home draws against the Swiss team and then Benfica that really niggled Ferguson.
"Finishing off games has to be a driving force for us," he said Tuesday. "I think we all agree we were careless in two of the games at home last season. The Basel game was the one where the criticism quite rightly lies. We were 2-0 up and playing well and then got careless in the second half and ended up drawing 3-3.
"Hopefully our home form, which had been good for many years, will be good again this year."
Braga, which is sixth in the Portuguese league, is playing in its second Champions League campaign after beating Italian side Udinese on penalties in the playoffs.
Cluj, the Romanian champion, travels to Portugal with a squad containing three former Braga players — Mario Felgueiras, Diogo Valente and Rafael Bastos — and six Portuguese players.
Cluj finished bottom of its group in its only two previous Champions League appearances, in 2008 and 2010.
"We want to get to the third place in the Champions League (group), although we'd really like to come first," Cluj owner Arpad Paszkany said. "It's just a theoretical chance, and we can compensate through giving it our all, luck and having a really good day."