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Football Association chairman Greg Dyke set that target in 2013 and Southgate believes it is still possible despite his side's early exit from the European Under-21 Championship.
"We need to be challenging regularly in semi-finals and finals of tournaments in the coming years," said Southgate.
"That, with coupled with experience at the top end of the Premier League, will bring a challenge for a World Cup."
A 3-1 defeat by Italy in the Czech Republic on Wednesday sealed a third successive first-round exit for England at the European Under-21 Championship.
Former England defender Southgate, who wants to remain as Under-21s manager, added: "2022 is the target and that gives us a goal to aim for.
"There are a lot of junior and senior tournaments before that moment. It is not an unrealistic timescale."
In the same speech detailing his World Cup goal in September 2013, Dyke also highlighted a "frightening trend" of the reduction in the number of English players in the Premier League.
Almost two years on, former Crystal Palace, Aston Villa and Middlesbrough man Southgate says young England players are getting more opportunities in the top flight.
"The landscape is improving," said Southgate. "There are several Premier League managers who are now giving opportunities to young English players.
"There is a lot of work going into youth development and we are seeing technically better players coming through.
"We want our young players to develop and being able to handle the ball is an important part of that.
"That is starting to come in all of our age groups, but until we get to semi-finals or finals more regularly that won't be the focus of attention."
England can win the 2022 World Cup, says Under-21s boss Gareth Southgate.