The Liverpool forward scored in the 39th and 85th minutes to condemn England to their second successive defeat in Group D, which leaves them close to a World Cup exit.
Suarez was doubtful for the game following surgery last month to repair a small meniscus tear but, after notching a brace in Sao Paulo, the 27-year-old says their side will now switch their focus to Tuesday’s crucial clash with Italy.
"This is incredible. I had told my team-mates that I had a dream that I was going to score two goals in this match,” he told Univision.
"We had to win this match and we did it playing like Uruguay does in these kind of games. Now we have to think about Italy, another very important rival.
"This victory is for all those people who said so many bad things about the team, it's for them."
Suarez says he endured a difficult spell on the sidelines following the injury to his knee, and has expressed his gratitude towards his family for their support.
He said: “People laughed about my injury, I had a very difficult moment. I thank my wife and children for enduring me."
Uruguay's centre-back Diego Godin admits it was 'beautiful' to overcome Roy Hodgson's side and says his team were always confident of getting a result in the Arena Corinthians.
"It was like a final for us, we feel like we won a decisive game and now we will enjoy it like the fans that were at the stadium," he said.
"We'll keep fighting until the end. We knew we could win today.
"The game against Italy will be another final."