Chesterfield hit back with a strong second-half display after debutant and Bolton loanee Conor Wilkinson scored from 12 yards to give the Reds a fourth-minute lead after a terrific run from teenager Danny Crowley.
Jay O’Shea levelled after the break from 15 yards, before debutant Sylvan Ebanks-Blake put the Spireites ahead. Sam Morsy made sure of victory a minute later with a 20-yard strike in off the post.
With defender Mason Holgate left out of the line-up as a move to a Premier League club moved closer, Johnson said: “I thought we started well and looked slick on the counter-attack. We got pegged back and once we got pegged back a few went down like dominoes.
“Over the course of 90 minutes, we did look like we capitulated.
“The second and third goals were really poor goals for us to concede.
“We have to grow up very quickly because this league is a tough league. We certainly have some improvements to make.
“There were some good parts to it but just not enough.”
Johnson, missing injured youngster James Bree, had four debutants in his young side, Marc Roberts, Alfie Mawson, Dan Crowley and Conor Wilkinson.
Summer signings Nick Townsend, Marley Watkins and Joe Rothwell were on the bench.
Chesterfield: Lee, Talbot (Raglan 80),Hird, Evatt, Jones, Gardner, Morsy, Banks, Ariyibi (Dieseruvwe 90), O’Shea, Ebanks-Blake (Gnanduillet 81). Unused substitutes: Humphreys, Harrison, Onovwigun, Cairns.
Barnsley: Davies, Scowen, Mawson, Roberts, Nyatanga, Smith (Rothwell 83), Crowley (George Williams 57), Pearson, Hourihane, Wilkinson (Watkins 57), Winnall. Unused substitutes: Townsend, Watkins, Rothwell, Maris, Williams, Digby, Phenix.
Referee: A Woolmer (Northants).
Man of the match: Sylvan Ebanks-Blake.