Bopara took England's best Twenty20 bowling figures during the win at the Kia Oval, claiming four wickets for the expense of just ten runs.
Previously in 2009, the 26-year-old struck three consecutive Test centuries against the Windies, only to see his form drop and his place in the side taken.
The Essex all-rounder has now claimed that he will not allow those events to happen again.
"I definitely feel more of an England player, especially over the last month," he told Sky Sports News.
"Long may it continue, but you can never bank on being around. I just want to take one step at a time and not get too far ahead of myself, because that happened when I got those three hundreds in a row.
"When you get above your station that's when you fall quite hard."
The final game in the series between England and the touring Windies takes place tomorrow.