United have won their opening two fixtures in Group H against Galatasaray and Cluj, but defensive injuries have hampered them somewhat, with Nemanja Vidic, Chris Smalling and Phil Jones missing most of the season so far.
And while Sir Alex has overseen the best period of the club's history in terms of trophies won, he admits being frustrated not to have won the European cup more times.
"It is a frustration that we have not won the Champions League more often, especially when I think of the times we've thrown it away," he told the Daily Mirror.
|A DECADE OF ROONEY
|10/1||Man Utd are 10/1 with bet365 to win the Champions League
"But you can't let it eat away at you. You've always got the next year. The final is at Wembley this season and that's a great incentive for us.
"If I can get my defenders back, we'll have a great chance."
Sir Alex also said that while Chelsea deserve credit for winning the trophy last season, he prefers his team to play a more expansive style of football.
He added: "The objective is to get through to the knock-out rounds. We want to do it the right way.
"I thought Chelsea carried a little bit of fortune in that they got goals at the right time in Barcelona. But you have to give them credit. They were very strong and did some great jobs, defending, and defending is part of the game, too. We have suffered for bad defending over the years.
"The most important thing is that we score enough goals to win a game and that's part of United. It's part of what this club is."