Spurs are seven points behind fourth-placed Manchester City and three of the clubs above them in the Premier League also have games in hand.
Rose believes that dropping points at home could ultimately cost Spurs but he has urged the squad to continue to battle.
"We've got to keep fighting until the end but it's going to be very hard to break into the top four," Rose told The Independent. "Man City have three games in hand, Liverpool are playing extremely well, and Chelsea and Arsenal are playing well as well. We might have to look to next season now.
"Some of the games we have lost and drawn at home, it's been unacceptable."
Spurs return to action against Southampton on Sunday.