Smith was replaced by Koskinen after giving up six goals on 25 shots. Koskinen stopped 20 of the 21 shots he faced in the Oilers' 8-6 loss.
It was the second Game 1 in a row in which Smith was replaced by Koskinen. He was pulled after giving up three quick goals in the Oilers' series-opening 9-6 loss to the Calgary Flames last round.
The next day, Woodcroft took a different approach than he did on Wednesday, confirming Smith would start Game 2 versus the Flames.
Woodcroft said Thursday that he believes Smith will do the work to improve.
“I think with Mike Smith you know what you’re getting," Woodcroft said. "You talk about someone who’s consistent in his process. Mike Smith is a true professional. He’s able to have a short memory on some things. He’s going to work to be the best he can be."
Woodcroft also had praise for Koskinen.
“I thought Mikko gave us a chance to win the game," he said. "He made some saves at the right time. We still weren’t as clean defensively as myself or our coaching staff would want. But he made some big saves.
"... We found a way to make it a 7-6 hockey game and we had a couple Grade As to tie it up. We didn’t do it. Sometimes you get what you earn in hockey and we weren’t as good as we needed to be. We all know that."
The Avalanche host the Oilers in Game 2 on Thursday at 8 p.m. ET / 6 p.m. MT on Sportsnet.