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Wanderers came from a goal down to beat Fleetwood 2-1 on Saturday and maintain their perfect start to the season.
Bolton were relegated from the Championship last term, but have won their first four League One games under new manager Parkinson.
"I thought it was our biggest test on Saturday," said Parkinson.
He told BBC Radio Manchester: "There was an edginess around the place. You could feel that, and that's understandable given what's happened in the past.
"The most important thing I'm pleased with is the character. You can have good players, but they've got to play when the pressure's on.
"I felt there was a little bit of pressure on us and we responded very well."
Bolton boss Phil Parkinson has praised his team's mental strength after they matched their best start to a league season in 82 years.