Jones revealed over the weekend he had agreed to terms with Rugby Australia (RA) regarding his exit, less than one year into a contract spanning the 2027 World Cup on home soil.
RA waited until Tuesday to confirm it had accepted Jones' resignation, about two weeks after the coach insisted he was fully committed to the Wallabies.
"I think we ended up at a sensible outcome and that's certainly something which we worked through over the last few days and we closed it out quite well," Waugh told a news conference at RA headquarters in Sydney.
"Eddie's put a lot into 2023 and into the (World Cup) campaign and the performances weren’t where they need to be," he continued. "I think that as the CEO, as Australian supporters, as Australians, we’re disappointed with the performances and we need to move forward from that."
Appointed in January to much fanfare in Australia - only weeks after being sacked as head coach of England - Jones led a youthful Wallabies squad to the World Cup in France, where they bowed out of the group stage for the first time.
The Wallabies were rocked during the tournament by reports Jones had interviewed for a coaching role with Japan two weeks before their first match. Jones repeatedly denied it.
Waugh said that he took Jones at his word and that the reports had not been a factor in his exit.
In an interview with local broadcaster Nine Network on Monday, Jones said he had resigned because RA could not commit "financial and political" resources to change Australian rugby.
Waugh said he was disappointed with the comments but acknowledged there were differences with Jones about the way forward.
"I've got to be fiscally responsible as to how we spend our money," said the former Wallabies flanker.
Waugh will lead the search for a third Wallabies coach in 12 months. The team has the British and Irish Lions tour in 2025 and the 2027 World Cup on home soil.
"I think it's a really good opportunity for any aspiring coach," he said. "We have a job to do here. We have a lot of ground to make up with building trust with our stakeholders and community, and we all know we have let down the people and we are ultimately responsible."
