The Barcelona star scored two superb goals in the first half before Fred and Fernandinho added two further strikes in the second period to secure top spot in Group A for the Selecao.
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"It was our best match not only by the end result but by the way we played on the pitch," he told reporters after the match.
"We are on the right track. We are progressing.
"There's no pressure. I've always said in my interviews that there is no pressure when you are realising a dream, something that you want from when you're tiny, and today I'm doing it. I'm playing games I've dreamed of all my life. I want to help my team-mates, to do what I can on the field to help Brazil become champions."
Brazil will now face Jorge Sampaoli's Chile in the last 16 of the tournament, but Neymar does not believe his side have gained an advantage by avoiding Group B winners Netherlands.
"Everybody is at the same level and football is becoming harder and harder. We are going to face a very strong opponent in the next match," he added.
"I think it will be a very hard match. Everyone knows that there are a lot of surprising teams. Watching the games, I cannot tell which is the weakest team in the competition."
Fred responded to criticism of his displays during the opening two matchdays with the third of Brazil's goals on Monday and he confessed it was a relief to get off the mark in the tournament.
"This drought was bothering me, and the bad performances. But I think we all evolved, as a team," he told TV Globo.
"This evolution during the World Cup was a natural thing to expect. We needed this evolution, and to show that aggressiveness we've shown before in this World Cup. Three, four players fighting for the ball - that's the kind of attitude we need."