The Red Devils were expected to force their way into contention for the crown this season having finished as runners-up behind record-breaking champions Manchester City in 2017-18.
They were, however, to endure a humbling slump under the guidance of Jose Mourinho before the Portuguese was relieved of his duties in December.
A revival has since been overseen by Ole Gunnar Solskjaer, with United having collected 10 wins from an 11-game unbeaten run under the Norwegian.
Such form has lifted them back into the top four and rekindled belief that there are better times to come.
Matic said of future ambitions: “To win the league you need to win the games as we did in the last seven, eight games.
“So you need to win six, seven games in a row, then you can drop some points, to draw, to lose one game.
“This is the way to fight so if we play like this for the next season then we will be one of the teams who is going to fight for the title.”
Matic knows what is required to lift the Premier League title having savoured two successes during his time at Chelsea.
He is still waiting on a first trophy with United having been snapped up by the Red Devils in the summer of 2017.
FA Cup and Champions League campaigns continue to be pieced together this term, with heavyweight fixtures approaching in both of those competitions.
The former is set to deliver a fifth-round clash with Chelsea and the latter a last-16 encounter with French giants Paris Saint-Germain.
Solskjaer will be hoping to see his unblemished record extended through those fixtures, with Matic hailing the belief that a Treble-winning hero of the past has returned to Old Trafford.
He added: “He's always positive.
“Of course, when we don't play well, of course, he needs to shout a little bit.
“But he's the same - always positive. The same when I see him at the press conference, he's like this with us also.”
United are set to play host to PSG on Tuesday before tackling Chelsea next Monday and welcoming Liverpool to Old Trafford in their next Premier League outing on February 24.