Johnson told BBC Radio Cambridgeshire: "I knew right from the off that he'd be hugely ambitious, but I'm feeling the same way and you need to aim high.
"Hopefully if I miss one or two of his targets I won't be on my way."
Posh have made seven summer signings including Northern Ireland international Grant McCann and Australian youngster James Wesolowski.
George Boyd has also been persuaded to sign a new long-term deal, despite interest from several clubs.
"I think we've had a decent pre-season, anything that didn't go well we worked hard on and we're ready to go," Johnson said.
"We know we've got quality individuals, they've got the right work-rate as a team and I know they're all ambitious."
Posh will be anxious to avoid an opening day defeat for the third season running against Bristol Rovers on Saturday.
Gabby Zakuani, Lee Frecklington and Chris Whelpdale remain on the sidelines, but Dave Hibbert is available for selection following the birth of his first child.
Kelvin Langmead and Ryan Bennett should line up in central defence with Charlie Lee at left-back.
"It's a long old season so everyone will get to play and feel they're part of what I'm doing here," Johnson said.
Source: BBC Sport
Source: BBC Sport