The Red Devils came from behind only to let a lead slip at the Bet 365 Stadium on Saturday evening.
The result ruined their prefect start to the season.
It means they are now joint top with Manchester City, but are above their cross-town rivals on goal difference.
And Matic says United have to make sure they win games like the one this weekend.
Matic told MUTV: “It was a tough game.
"To be honest, it’s always a tough game when you come to this stadium.
“Stoke are a good team, so it was difficult, but we managed to get a point.
“If we want to be champions, we have to win games like this because in these games, if you win, you are champion.
“We have to know against teams like this you have to have a little bit more, you have to be concentrated and of course we’re not happy with a point.
“It’s always important if you can come from behind, and I think we showed spirit.
"We had the lead in the second half but they scored a goal from the corner kick.”
United have the chance to prove thier European pedigree this week when they take on Basel in the Champions League.
