Beckham and Sir Geoff Hurst, though, defended Sterling's displays after the quarter-final win against Sweden.
Although Jones acknowledged that the 23-year-old's movement and positioning had been fine during the tournament, he appeared to question how good he'd be were it not for his blistering pace.
Everyone is talking about Raheem Sterling right now.
Croatia coach Zlatko Dalic has identified Raheem Sterling as England's danger man in the World Cup semi-final on Wednesday.
Sterling has never been a popular figure in England, with many Liverpool fans still not over his acrimonious departure to Manchester City two seasons ago.
England survived a penalty shootout against Colombia in the last 16 whereas Croatia emerged through extra-time and spot-kicks against Denmark before going through the same ordeal again against Russian Federation in Saturday's quarter-final. "He offers so much to the team", the Tottenham midfielder said.
It seems likely Sterling will keep his place for England's first semi-final in 22 years - when Southgate himself missed a penalty in the Euro 96 shootout against Germany.
"I wouldn't say there are any glaring weaknesses (in England's team) since they are in the semi-finals, that says it all".
Despite excelling at Manchester City this season, scoring 23 goals in all competitions, the 23-year-old has come in for criticism for his displays in Russian Federation. Off the ball his work rate is incredible.
To do so, and seal their first World Cup final in 52 years, England will need to see off a Croatia side who thrashed Argentina in the group stage and edged Denmark and Russian Federation on penalties to reach the last four.
After a quiet opening World Cup game against Tunisia, there was speculation Sterling would be dropped for the following group match against Panama.
"Every player wants to win the World Cup, every country wants to win the World Cup, so anything less than that is not really a bonus". By starting Sterling, England have a better plan B late in the game.