Matic, who joined United from Chelsea last month for a fee of £35m, has been a key player for his new side so far this season, with his presence in midfield helping United to three straight Premier League wins and three clean sheets to start the new campaign.
But the Serbian international had grander ambitions than simply adding to the two Premier League titles he won during two seperate spells with the 'Blues', with the 29-year-old keen on tasting Champions League success as well.
'Winning the Premier League title will be a tough task not just for us but for everyone because there are five or six realistic contenders,' he explained.
'But we all know that Manchester United are expected to win every game. As far as the Champions League is concerned, we've had a favourable draw and we are hopeful of still being in the competition in the latter stages.
'The 2-1 UEFA Super Sup defeat against Champions League holders Real Madrid was a good test of our credentials to slug it out with Europe's best.
'We were outplayed but that was a one-off while the Champions League is a competition where you face different rivals in every round.'
Can United compete with Europe's best? Their start to the new season certainly suggests that Jose Mourinho's side has improved significantly since the end of last season.