"The team was not responding to Kevin," Morey said Wednesday. "There is no time in the West.
"It's not just losing. It's not just 4-7. It's the way we're losing, by how much, by how the team is responding. It was tough. This is not something we take lightly. This is a decision we thought about a long time. We knew we were under the gun."
The Rockets, with the league's second-worst defensive team, are currently on a four-game losing streak that prompted a players-only meeting on Tuesday morning, following a 111-95 loss to the Boston Celtics on Monday night.
"We were starting to address some of the issues that were the reason I was let go," McHale told the Houston Chronicle after his firing. "We just weren't playing with any juice, with any rhythm. We haven't been able to get the problems solved. We probably had more meetings in last six weeks than in my previous four years here. It wasn't working."
The 57-year-old McHale signed a three-year contract extension last December, worth more than $12 million guranteed.
McHale, a Hall of Fame player, was hired by the Rockets before the 2011-12 season. He was 193-130 overall with the Rockets, including three straight trips to the playoffs and a loss in last season's Western Conference finals.
All-Star guard James Harden is averaging 27.3 points for the Rockets, but he is shooting only 37.2 percent from the field and 26.2 percent on 3-pointers.
Rockets players praised McHale during their playoff run last season, calling him a player's coach.
"I felt like I was talking to an actual player,'' Harden said in May. "Obviously he's won championships so he knows what he's talking about. So my ears are just locked in and focused in on what he's saying.''
Rockets owner Leslie Alexander said he is disappointed in the team's performance so far this season.
"The team was obviously not responding on offense," Alexander said. "On defense we weren't playing hard. It continued for a while. I've never seen my team play as poorly and with less effort. I'm not attributing it to the coach. I had to do something."
The general manager was asked if Bickerstaff, who is the son of former NBA head coach Bernie Bickerstaff, would be the coach for the remainder of the season.
"J.B. is great with players, great with schemes, and he's been preparing for this his whole life," Morey told USA TODAY Sports. "He obviously has a great pedigree, and was critical to our winning over the last four years with Kevin. He architected the defense last year that was top 10 overall and top five when Dwight (Howard) played. Job One, really, is we've got to shore up our defense, and I believe J.B. can do it.
"J.B. is the interim head coach and we believe in his ability to turn this around and lead us going forward."