Edmonton has lost seven of its past eight games (1-7-0).
"We weren't detailed defensively, I think we got beat a couple of times," Khaira said. "They came out and pushed and we didn't have a response. We need every win we can right now, but those ones hurt. We're up 2-0 and they score three. There is not much to be said, we need to be better."
Strome scored at 18:29 of the first period to give the Oilers a 1-0 lead.
With the teams playing 4-on-4 because of coincidental penalties to Bruins defenseman Torey Krug and Oilers defenseman Brandon Davidson, Strome collected the puck off the boards in his own zone, skated down the left side and shot through Khudobin's pads.
Khaira made it 2-0 at 11:38 of the second period on a 3-on-2 rush. Khaira took a pass from Anton Slepyshev in the slot and shot it over Khudobin's glove through a screen.