"They shoot the ball so well and when they run, they can capitalize very quickly," Williams said. "We just got beat up in the fourth quarter and weren't able to come back."
Chandler Parsons finished with 10 points and 10 rebounds for Houston, and Jeremy Lin had nine points and seven assists.
In addition to Anderson, Jason Smith and Brian Roberts also scored in double-figures off the bench for New Orleans.
New Orleans was without guard Eric Gordon, who had spent most of the season recovering from a knee injury before making his season debut last Saturday. Gordon scored 11 points Tuesday night, but Williams rested him as a precaution and said he expected Gordon to return when the Hornets visit Dallas on Saturday.
Rookie Austin Rivers started in place of Gordon and finished with only four points and one assist in 17 minutes. Rivers made just one of six free throws, and New Orleans finished 11 of 20 from the free throw line.
"We have some young guys who have never been in this position before and they're overwhelmed," Williams said. "I wish the season started today because we'd be in a lot better shape, record-wise. Guys are frustrated, but I see tons of growth and this is going to help us going forward."
The Rockets visit Milwaukee on Friday to begin a stretch where they will play nine of their next 11 games on the road. Houston is 5-8 on the road and 13-6 at home.
Notes: Houston announced Wednesday the signing of G/F James Anderson, who averaged 3.4 points and 1.4 rebounds in 9.4 minutes per game in 10 games this season for San Antonio. The Spurs waived Anderson on Dec. 20. To make room for Anderson, the Rockets released G Daequan Cook.