United lost the FA Cup final to Chelsea on Saturday and finished second in the Premier League, 19 points behind Manchester City.
That follows the club spending £148m on transfers last summer, including big-money signings Matic and Romelu Lukaku.
But Matic believes they can “fight for the title and Champions League” if they sign experienced players this summer.
“The only team who is better than us this year is Man City,” said Matic, 29.
“Obviously, they play amazing football. But we are second and we are in the Champions League next year, which is the most important thing.
“I think we need some players with some experience to bring some more qualities to our team.”
United have spent £261.67m over the past two seasons – £98.37m less than City – with a world record £89m fee paid for Paul Pogba in 2016.
Striker Lukaku, 25, joined for £75m last summer and Matic moved to Old Trafford for £40m.
There were also other expensive deals including moves for Victor Lindelof, 23, and Eric Bailly, 24, while Alexis Sanchez, 29, moved from Arsenal in January.
United last won the title in 2012-13 in Sir Alex Ferguson’s final season in charge and have since finished seventh, fourth, fifth, and sixth before their second-placed finish this season.
