Last season, David Moyes' side managed to snap up a draw in the same fixture, but failed to do so again last weekend, despite having dominated the game.
Rodwell was frustrated at the final score, and believes that his side were good enough to beat a declining Manchester United, saying they "weren't the same side" as before.
According to reports in the Sun, the Englishman raged: "They managed to keep us out of their penalty box, but they weren't the same side either, and we definitely think it is a chance missed.
"In the second half we were pushing forward as they sat back a lot. We just lacked that creativity in the final third.
"We had a lot of possession and they were there for the taking, but we didn't capitalise."
Rodwell believes that their 6-1 spanking by Manchester City has led to Sir Alex Ferguson seeking more a more cautious approach, which was evident in the way Wayne Rooney was pulled back to play deeper in midfield.
He revealed: "He (Rooney) dropped off very deep today, and we didn't expect him to play there.
"He's top class, but we managed to stop him getting as much of the ball as usual, so really he didn't have as much effect as he could.
"We expected them to press a lot higher up the pitch, but we didn't capitalise the way we should have done.
"Obviously they'd looked at the goals they conceded last week when players were bombing forward.
"Maybe they felt vulnerable and they didn't want to go as gung-ho", the Everton star concluded.