The Millers, who won promotion from League Two last term, have drawn their first two games, against Crewe and Preston, while ceremoniously dumping Sheffield Wednesday out of the Capital One Cup.
Evans, who returns to the scene of past glories at Crawley at the weekend, is unperturbed by their failure to register a win and is satisfied with his side's showings.
"It has been a reasonable start," he said. "We will always judge it on performances, I know results ultimately get you sacked, but we are pleased with the first two games.
"We won the first game last season and then went to Northampton and got beat and there was a crisis. It's 46 games, it's a long season, there's no need to panic.
"The 0-0 game against Preston last week was the first 0-0 draw at New York and we had the lowest number of draws last season, so we don't draw many games."