The Lakers have now lost five of six games since superstar LeBron James suffered a groin injury in a Christmas Day victory over two-time defending NBA champions Golden State.
With three key contributors absent, Walton said, he wanted to see more intensity from the players who were on the court.
"We need more passion, we need more fight," Walton said. "That's not scoring more, that's more diving for loose balls, communicating loudly.
"It's hard to win in this league when you're healthy, so you've got to give double that effort when guys are down."
The Timberwolves, led by Karl-Anthony Towns's 28 points, 18 rebounds and four blocked shots, seized control immediately and led by 16 points after the first quarter.
"I think offensively our guys were trying to play the right way, we just weren't making shots," Walton said of a first quarter in which the Timberwolves out-scored Los Angeles 35-19.
"But defensively it's unacceptable that we let (them score) that many points. That's the second game in a row a team has come in the first quarter and just scored at will on us."
Only four Lakers players hit double digits, reserve Lance Stephenson leading the charge with 14.
Brandon Ingram added 13 points but connected on just five of 16 shots from the field.