It was the first time this season that Anaheim has led by more than a goal entering the second period.
"You get in a hole like that, and when the other goalie at the other end is hot like he was tonight, that's a bad formular for us," DeBoer said. "That came back to bite us."
The Ducks, who entered the game ranked 30th in the NHL on the penalty kill (70.5 percent), went 4-for-4 against the Stars' power play, including killing one off over the final 1:55 of regulation to preserve the shutout.
"Definitely goaltending has been a big key in this little stretch that we've been having here," Ducks forward Jakob Silfverberg said. "We've kind of been doing the right stuff all throughout the year, but it just hasn't really gone our way. ... We're pushing at the right time, we're working as a four-man unit out there, but obviously we've been having some unfortunate bounces."
The Stars will return home for three days before hosting the Florida Panthers on Sunday.
"We have a lot of days off coming up here," Dallas forward Tyler Seguin said. "Get some good practice days in and just reset and refocus and definitely move on from this."