Former goalkeeper Pat Bonner believes Celtic have been too slow off the mark in the transfer race, and his one-time team-mate Murdo MacLeod more pointedly accused the club of selling out.
Celtic have picked up £33m in prize money from the Champions League in the past two seasons and the club announced pre-tax profits of £21.3m earlier this year.
The sales of Victor Wanyama, Gary Hooper and Kelvin Wilson last summer contributed to the figures and Bonner is concerned the club will find it difficult to hold onto Fraser Forster and Virgil van Dijk.
Regardless of the outcome of this morning's UEFA disciplinary hearing, which will determine which tournament play-offs Celtic gain access to, mistakes in their close-season strategies have been identified and Andy Walker believes the board have been too reluctant to back Deila with spending power.
Only out-of-contract keeper Craig Gordon, who has not played a competitive game for over two years, has been signed while Cardiff City forward Jo Inge Berget joined on a six-month loan deal, neither featuring against Legia.
Walker believes distress signals in the group stages of the Champions League last season where Neil Lennon's side finished bottom of their section, have not been addressed. He told Sky Sports News: "Last season they were drawn against Barcelona, AC Milan and Ajax. They struggled against all three and the supporters knew then that the team had to be strengthened.
"Instead, Celtic have got rid of a big European player in Georgios Samaras and failed to make any sort of effort to replace him. They have also failed to support the new manager.
"Obviously, he is due a bit of criticism, but I just don't think he was helped by the lack of support he has had from the board. Celtic needed to strengthen and they have failed to do so at a vital time.
"Clearly, Celtic need to spend a bit of money. They have to try and get some players in with a bit of excitement just to lift the supporters.
"They know they will watch a team who will win the title this season, but I think when Ronny Deila came in he said they would play with energy and drive and I think he needs new players to try and achieve that."
The most worrying aspect of Celtic's defeat to Legia was the eventual margin of defeat - 2-0 at Murrayfield compounding a 4-1 defeat in Warsaw - and Michal Zyro, who scored the opener on Wednesday, believes the SPFL champions played right into their hands.
"We didn't expect to dominate Celtic, but we knew how we wanted to play it. And they played exactly how we wanted," said Zyro, who paid tribute to manager Henning Berg.
"They had a lot of the ball in the middle of the pitch, which we knew they would get, but they did nothing with it. We defended so well, they had absolutely no chance of scoring. And that's all down to our manager. He had a plan for the match and it worked out perfectly for us.
"To beat such a renowned team as Celtic 6-1 is special. But we proved we are a fantastic team. The Scots tried to dispirit us. They were very verbal and tried to make us afraid. But we ignored them and focused on ourselves. The manager made us mentally strong - he told us to believe in ourselves even after the home draw with [St Patrick's Athletic]."