This is because they were beaten by Barcelona in two of the three finals they reached.
The record books may show the current spell to be United's most successful ever in Europe, but Ferguson insists they need to take that final step and win the Champions League trophy outright again in order to make such a claim.
United will resume their European campaign at home to Basel on Tuesday night - when they will be without leading strikers Wayne Rooney and Javier Hernandez due to injury - with Ferguson insisting his players need to strive for even better.
Ferguson said: "The Champions League is the best competition in the world now, better than the World Cup, better than the European Championships, it's a fantastic tournament.
"But it's not a golden period for us because we have lost two finals, so I don't think it can be called a golden period.
"We have been consistent in the Champions League, our form away from home has been outstanding and we hope we can do better this year and win it, that's the aim of this club all the time."
Ferguson confirmed that Rooney would miss Tuesday's match with a hamstring injury and said that it was difficult to know when the England striker would be back in action.
"He's not playing tomorrow. It's difficult to assess with hamstrings but we hope we have him back quickly. He did a bit of jogging this morning but that's all," said the United boss.
Ferguson also said that Hernandez's dead leg would keep him out against Basel but that the Mexican should be back for when Norwich visit on Saturday.
Michael Owen and Dimitar Berbatov are likely to lead the attack against the Swiss club, though the fit-again Danny Welbeck could also feature - with Rio Ferdinand partnering Phil Jones in central defence.
Basel won their opening fixture in Group C 2-1 against Romanian side Otelul Galati.
But they have never won in seven visits in all competitions and since drawing against both United and Liverpool on their Champions League debut in 2002 they have lost to Newcastle, Middlesbrough, Blackburn and Fulham.
"Manchester United have strengths offensively and I count them as one of the sides to win the competition," said coach Thorsten Fink.
"We have experience and young players but what we don't have is fear.
"We are a Champions League team, we know what we can do, we have confidence.
"We haven't come here to sit and watch, we have come here to play.
"We are looking to get something out of the game but we have to be tight at the back."
Xherdan Shaqiri completes a two-game ban while fellow midfielder Benjamin Huggel is also suspended after his red card against Otelul.