"The Lions is like a start of a new season. You want to get your game going as quick as you can," said Wilkinson.
"I'll have to see how I react to the pressure of a Lions home game in Cardiff. "I like the idea of going out there and getting more experience under your belt. It is like putting money in the bank, it is always there for you.
"Even if you end up losing, it is still experience. The more of that you can have the better."
Wilkinson may have been added to the squad late due to fitness worries, but Woodward and his midweek head coach Ian McGeechan immediately made him vice-captain for Monday's game.
"With the vice-captaincy is an opportunity with a lot of responsibility," said Wilkinson.
"There is a responsibility on everyone to learn quickly, learning how to play with each other, learning the principles and ideas and ways we are trying to train so we can see what we need to work on," Wilkinson said.
"The biggest thing about this game is to get a successful result. Looking at the format of the tour, trying to get a successful result every time we play moves the tour on, makes us so much stronger for the next games.
"The responsibility is there to go out and try and win and show that collective spirit, that we are one team."