Instead, a heartbreaking loss on a last-second 3-pointer ended their season in the first round - just as it did a year ago.
Damian Lillard made a 3-pointer at the buzzer to lift the Trail Blazers to a win on Friday night to take the series 4-2.
''It's a tough loss, but it's something we've got to learn from,'' Howard said.
This year's early exit comes after the Rockets lost to the Thunder in the first round in 2013 in their first playoff appearance since 2009.
Howard spurned the Lakers to sign a four-year, $88 million contract with the Rockets with a singular goal of winning a championship. Houston gained the No. 4 seed in the Western Conference but quickly fell into a 0-2 hole against the Trail Blazers, and it was too much to overcome.
''Nothing is easy,'' Howard said. ''I've been to the finals. I've been to the Eastern Conference finals. I've been to the top and it's not easy getting there. You've got to make everything count. I think that's a big lesson for us all.''
Howard had a solid first season in Houston after one disappointing year in Los Angeles, and averaged 18.3 points. He was fourth in the NBA with 12.2 rebounds a game. He improved in the postseason when he averaged 26 points and 13.7 rebounds a game.
James Harden embraced a bigger leadership role in his second season in Houston and again led the team in scoring. But his shooting woes in the playoffs were a factor in the early demise of the Rockets. Harden scored 34 points on 60 percent shooting in Game 6, but made just 41 of 118 shots combined in the first five games.
''It's tough right now,'' Harden said. ''Our season is over so guys are looking back on it and are frustrated.''
The game was particularly wrenching for Chandler Parsons, who was late getting over to cover Lillard on the winning basket.
''This is the worst feeling I've ever had in my life,'' Parsons said.
Houston lamented missed opportunities after three of its losses were decided by less than three points and two of those defeats came in overtime.
''It's a learning experience for a lot of these young guys on our team that each possession counts in the playoffs,'' Howard said.
The Rockets got a boost this season from the development of Terrence Jones in his second year. Jones played sparingly as a rookie before becoming a starter in 2014. He averaged 12.1 points and 6.9 rebounds in 76 games.
He joins point guard Patrick Beverley and Parsons as a trio of Houston starters with three or fewer years of NBA experience.
The Rockets got an up-and-down season from Jeremy Lin, who lost his starting job to Beverley. His inconsistent play continued in the postseason. He had four points and three turnovers in Houston's Game 4 loss before coming off the bench to score 21 points and spark the Rockets to a win in Game 5 with Beverley battling an illness.
As the Rockets tried to move on from their disappointing finish, they took some solace that this team should remain virtually intact.
''We've got a great nucleus of guys,'' Howard said. ''Everybody has to come back better next season and see the mistakes we made this year as a team and try to learn from them so next year we won't have situations like this.''