Prior to his switch to the Saints, the 26-year-old forward was linked with a move to Newcastle. According to a report in The Daily Mail in January, the Magpies were interested in Austin.
However, the former Burnley star joined Southampton instead, and ex-Newcastle midfielder Jenas has criticised the club for not signing him.
The former Nottingham Forest and Tottenham Hotspur star believes that signing Austin would have saved Newcastle from getting relegated to the Championship.
“The opportunities they missed to sign someone like Charlie Austin have come back to haunt them,” Jenas wrote on Yahoo.com.
“I don't know if Charlie didn't want to move to the north-east, or whether the club didn't show enough commitment to sign him, but that's exactly the sort of player they were crying out for all season.
“The club have gone down because they don't have a goalscorer in the ranks, which is ridiculous considering there were various options out there, and unacceptable for a club the size of Newcastle.”
Austin scored 18 goals and created 23 chances in 35 Premier League appearances for QPR during the 2014-15 campaign.
The Englishman scored 10 goals and created 17 chances for Rangers this season before his switch to Southampton in January.
The forward has struggled with injury problems at the Saints, and has scored one goal and created one chance in six Premier League appearances.