Game 2 of the best-of-7 series will be here Saturday.
"It's definitely a different looking team, different system, but we just, overall weren't good enough," Draisaitl said. "It's not even close to how we play and how we successfully play. We've got to move on, and we'll be better."
Ivan Barbashev scored twice, and Mark Stone and Jack Eichel each had a goal and an assist for Vegas, which is the No. 1 seed from the Western Conference. Laurent Brossoit made 23 saves.
"We were terrific," Brossoit said. "Another collective effort from all of us, right up and down the lineup. We had a lot of big nights from a lot of guys. … We took it to them for 60 minutes. I even think the score wasn't necessarily indicative of how well we played."
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Connor McDavid, Zach Hyman, Evan Bouchard and Mattias Ekholm each had two assists for Edmonton, which is the No. 2 seed from the Pacific Division. Stuart Skinner made 28 saves.
"I don't think our team was anywhere near what it needed to be to walk away with a road win in the playoffs" Oilers coach Jay Woodcroft said. "Leon had a great effort. He's been good all playoffs here, but our team can do things a lot better than we did tonight. … We had a chance, but there are things to clean up the goals against."