The National League newcomers won 1-0 at Ebbsfleet United to get life out of the EFL off to a great start.
But Allen, taking charge of his first competitive match as the club’s manager, didn’t think he side were much cop in Kent.
“I didn’t think we played very well,” he told the club’s website after Zavon Hines’ winner.
"First half I thought we were awful, but second half I thought we played better. Credit to the players for stepping it up - they had to.
“I haven’t come here to mess about, I’ve come for some action and that’s what they’re going to get.
“The substitutes that came on did very well for us. It’s a squad effort, the players on the bench were very committed and very strong with their voices to support the players.”
Chesterfield next face Aldershot at the Proact Stadium on Tuesday night.