Atletico had been on the brink of signing the France international until they lost an appeal against their transfer ban to the Court of Arbitration for Sport (CAS) on Thursday.
Diego Simeone's side are now unable to sign players until January 2018 at the earliest, complicating the future of Lacazette as well as their star man Antoine Griezmann, who had previously been strongly linked with a move to United.
"Real [in 2016] and Barca [in 2015] saw their punishments reduced with a favourable decision, but it wasn't the case for Atletico," Aulas said to L'Equipe.
"Of course, that has changed everything. This is bad news and good news. It was, in financial terms, a very significant transaction.
"We had given Alex the green light to go to Atletico, the club of his heart.
"I've not had his agent on the phone, nor him, as I've been in Cardiff [for the Women's Champions League final].
"But I had said to Alexandre not to get too far ahead of himself, as there can always be disappointments in football.
"It brings into question the commitments made on both sides. We had made progress on possible solutions."
This ruling is unjust, poses an unfair disadvantage in comparable cases and causes an irreparable damage to our club https://t.co/vhWpztBZVY— Atlético de Madrid (@atletienglish) June 1, 2017
As of today, we will work to close the ongoing operations as soon as possible and register players on January 1st https://t.co/vhWpztBZVY— Atlético de Madrid (@atletienglish) June 1, 2017
Aulas refused to entertain the prospect of loaning out Lacazette until Atletico are able to sign again in January.
"No, it's not possible," he said. "Technically, it's not. The solution would be for him to stay here until the ban is over.
"Football has a magical ability to throw everything up in the air. We might have one extra striker next season."
The prolific Lacazette has scored 91 goals in his last four Ligue 1 seasons.