John Mousinho conceded that his side could have no complaints about falling at the first hurdle to exit the Emirates FA Cup.
Tom Naylor converted a fine free-kick from Liam Mandeville to send Chesterfield into the second round at the SMH Group Stadium.
Pompey had a lot of possession as they sought a leveller, but rarely troubled Harry Tyrer between the sticks.
And Mousinho felt that the National League leaders fully deserved their place in the next stage of the competition.
The Blues boss said: “It’s difficult to pinpoint one or two moments because there were a lot of things that went wrong for us.
“Ultimately, our performance levels just weren’t there and we got beaten by a very good Chesterfield side.
“There were plenty of things we did well up until half-time, but they were all over us after the break and thoroughly deserved the win.
“Our quality was really poor and we got into some good spots, only for the ball to keep going out for goal-kicks.
"Ultimately, our performance levels just weren’t there and we got beaten by a very good Chesterfield side."
“We didn’t get too many shots off to test their goalkeeper and it was a frustration. We also got out-worked and it felt like they were running all over us at times.
“It can be difficult with the emotion after the game and you don’t want to overreact – which we won’t do – and sometimes it’s just best to take a breath.
“It’s a bit of a cliché, but these things happen in the FA Cup and the most important thing for us is the league campaign.
“That’s probably the first time we’ve taken our foot off the gas for prolonged periods and we got what we deserved.”
To compound Pompey’s misery, both Regan Poole and Tino Anjorin limped from the pitch during the first half.
Mousinho said: “Regan twisted his knee, but it was offside. The linesman slipped and decided not to give it, which was strange.
“It could have been prevented, although he came and sat on the bench with us in the second half and didn’t think it was anything too serious.
“Tino has hurt his hamstring, so we’ll have to see where we go from there. The other changes were just tactical.”