Wilshere made his first start in almost a month on Tuesday evening, with the Cherries securing a huge 3-0 win over their Swansea City.
Speaking after the game, Woodgate said: "I felt on top against Preston, I felt on top against Barnsley. You're looking for the players to really step up.
"It's more a mentality thing to stamp your authority on the game.
"I thought in the second half against Preston we didn't do that. I thought against Barnsley we didn't do that.
"(Against Swansea) we did that and we kept on playing. I want the lads to put their foot on the ball and play. I don't want them to just boot it.
"We put our foot on the ball and we played. I think that was at times down to Jack Wilshere.
"He did that. He had that calming influence in the game and just put his foot on it and played the simple pass.
"Sometimes the simple pass is the hardest one to play. He does that and I thought he was brilliant."
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