A vote on EFL Trophy changes may not have even gone ahead had clubs known some Premier League sides might reject the invitation, says Cambridge chief executive Jez George.
Arsenal, Liverpool and Tottenham are among six to reject the chance to enter an under-21 side in a one-season trial.
EFL chief executive Shaun Harvey says the Trophy needed change to "survive".
"I'm very, very surprised the package wasn't secured with the bigger clubs before it went to a vote," said George.
He told BBC Radio Cambridgeshire: "If you'd have told the EFL clubs that maybe some of those clubs wouldn't even accept the invitation, I'm not sure there'd have even been a vote, let alone a vote being the same way."
For 2016-17, the competition has been extended to 64 teams, with sides from 16 of the 21 category one academies joining League One and League Two clubs in 16 regional groups of four for the opening round.
Premier League champions Leicester, Chelsea, Southampton and West Ham are among the sides to have accepted the initial invitation.
The U's voted in favour of the proposals at the English Football League's annual general meeting in Portugal in June, as did Peterborough United.
However, Posh chairman Darragh MacAnthony says he would not have done so had he known the line-up of under-21 teams.
He said on Twitter: "If I had know such large amount of them (Championship under-21 sides), then no chance (of voting in favour). You live and learn. Now we have to get on with it."
Oxford United reached the final at Wembley last year before losing 3-2 to Barnsley, and their manager Michael Appleton firmly believes academy sides should not play in the competition.
"No, not at all," he told BBC Radio Oxford.
"That's just my opinion. I could elaborate, but I'd be here all night if I did.
"I don't think it's a good idea and it certainly wouldn't be something I'd be looking to do if I was in charge of it."
Cambridge have been drawn in Northern Group G alongside Middlesbrough's under-21s, Shrewsbury and Scunthorpe, which means combined trips of 458 miles.
George admitted that the competition needed to be "revamped", but that the group ties for his club may not be what is needed to boost attendances.
"They're three tough games against three good clubs but commercially I'm sure there could have been better draws for us," he said.
"In this competition early on you want to play local clubs that capture the imagination a little bit. There's no point in me saying these three ties are going to capture the imagination, because they're not."
One reason for Premier League clubs to have rejected the invitation was because the competition weeks fall during international breaks, when a number of under-21 players will be representing their national team at various levels.
George continued: "It just seems to me a general premise that if you want to invite the biggest clubs in the country to put their under-21 team in the tournament you make sure they'll accept the invitation.
"It seems fairly basic to me, and you make sure the dates the games are scheduled for fit them, because if you're asking them to come and create a big talking point and the whole point is they'll add to the competition, it doesn't help the status of the competition if they decline the invitation."
Southend United chief executive Steve Kavanagh also said it was "clear" that the competition needed "refreshing", but told BBC Radio 5 live that the withdrawal of Premier League teams left "a very bad taste".