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.
"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."
