The small forward agreed a three-year deal worth a reported $45m (£26.3m) with the Dallas Mavericks earlier this month, ending his three-season spell with the Rockets.
Howard told The AP: "It won't affect us at all. We have myself and James [Harden]. We have the best center and the best two guard in the game on the same team. It's on us."
Parsons averaged 16.6 points per game in 74 appearances for Houston during the 2013-14 season, rising to 19.3 during the playoffs.