"It's obviously really big in the context of the series," Stokes said. "We knew we needed to win this one to keep alive our hopes of winning the Ashes, so it's a good win. If you look at the first two games in terms of how tight they were, getting over the line in another tight game can mentally help, knowing that it's another close game but we've got over the line in this one.
"The first two didn't go our way. If you sort of flip it round and we didn't win this one and it's tight again, you would think, 'It's just not meant to be'. We're obviously over the moon that we won this one but it's just the start of what we know we need to do."
England made three changes to their side ahead of the Headingley Test, in part due to Stokes' own fitness issues. All three of the men who came into the side - Woakes, Wood and Moeen Ali - played important roles, taking 15 wickets between them and producing cameos with the bat.
"Woakesy, being out of the team for such a long period of time, and to come back in and perform the way that he did both with ball and with bat… seeing Woody running in like he does, big smile on his face and enjoying every moment out there was great," Stokes said.
"[And] I said before the series started that we decided to go with Mo back into the squad because of the impact he can have on games. I've played a lot of games with him and I know the impact he can have on his best days.
"You look at that little spell yesterday with 15 minutes when he took the wickets of Marnus [Labuschagne] and Steve [Smith] and that was a huge point in the game. That's Mo as a cricketer. You bring him into the team and you want him to be impactful with the ball and the bat and he certainly was with the ball this game."
Stokes also praised Brook's innings on the final day. "The way Brooky controlled the game from ball one with the bat was amazing," he said. "He went out there and put the pressure straight back on to them.
"The way he played with Woakesy in that partnership was high-class; for such a young lad in a high-pressure situation in the Ashes, it was incredible. We've all seen what he can do with the bat. He's an incredibly gifted player, and I think he's only going to get better and better, the more pressure situations he's put in."
Stokes was pleased with England's approach across the four days at Headingley, but insisted: "I still think we can be better." He added: "The thing about cricket is no-one has the perfect answer to everything. Everything will be assessed on the outcome. That will always be the case. No-one ever has the perfect answer for how it should be played.
"We can be better in certain areas, and that's all we can do, keep trying to be better and better and as clear as we possibly can as a team. People always seem to have an answer after the fact. I don't think anyone will ever crack it; that's why it's such a great game."
"We've kept the series alive and we just have to park everything from this week, but continue the way we play," Stokes added. "I said last week we find ourselves in the perfect position with the way we play cricket.
"It doesn't change. After the Lord's game and before this game, before the game in Manchester, we just have to do exactly the same thing: play cricket that gets a result, our way."
Matt Roller is an assistant editor at ESPNcricinfo. @mroller98