"It won't affect us at all," Howard said Friday of Parsons signing a three-year, $45-million deal with the Dallas Mavericks.
Parsons was a three-year starter that complemented Howard and guard James Harden.
"We have myself and James," Howard said. "We have the best center and the best two guard in the game on the same team. It's on us."
Howard, who spoke at his father's 10th annual Howard/Howard basketball camp in Atlanta, said he wishes his former teammate well with the Mavericks. But Howard said he and Harden will be able to carry the load without the 25-year-old Parsons, who had career highs with 16.6 points, 5.5 rebounds and four assists for the Rockets last season.
This has been a busy offseason for Houston. The Rockets hosted Carmelo Anthony before making a four-year max contract offer to Chris Bosh, but Houston was unable to sign any of those major free agents.
Howard, 28, said the addition of Ariza was "big" for the Rockets.
"He'll go through a wall for you," Howard said of Ariza, who was his teammate on the Orlando Magic. "Just to have soldiers on your team like that is great. We have that one-two punch with me and James. We're filling out our roster with guys who are willing to go through that wall and doing whatever it takes to win."