Roy Hodgson opted for the 18-year-old rather than Cole, a move that saw the Chelsea defender - capped 107 times for his country - announce his international retirement.
Shaw has impressed for Southampton in the Premier League this season and will vie with Leighton Baines for the left-back place in England's opening game with Italy in Brazil on June 14.
The defender was not expecting the call for the England coach, but has assured Hodgson that he will be ready to perform as and when required.
"I was very surprised," he said on Friday. "With Ashley Cole not playing many games (for Chelsea) I thought I may be in with a chance. But I think he played the last three games in the season and he played incredibly well.
"It made me think that maybe this is not my time, but obviously I saw I was announced in the squad and it was the best feeling in the world.
"I don't really feel pressure. I just focus on my own game. I have come here to help the England team and I will do everything I can.
"I feel ready if Leighton does pick up an injury. I don't think Roy would have picked me if he didn't think that."
Shaw made his England debut in the 1-0 win over Denmark in March when he came on as a second-half substitute for Cole.
