The Three Lions have now lost consecutive European Championship finals after missing out on penalties to Italy on home soil three years ago.
Southgate, whose contract expires at the end of the year, also led England to the 2018 World Cup semifinals and the quarterfinals four years later in Qatar.
But he has not been able to end his nation’s long wait for major tournament glory that stretches back to the 1966 World Cup.
“I need to have those conversations with important people behind the scenes and obviously I can’t discuss that publicly first,” said Southgate on what his future holds.
“Without a doubt, England have got some fabulous young players and even the young ones now have got a lot of experience of tournaments.
“Many of this squad are going to be around in two, four, six, eight years’ time. We have now been consistently back in the matches that matter, so it’s the last step that we haven’t been able to do.”
Despite reaching a first-ever major tournament final on foreign soil, England never managed to live up to their hype before the competition as pre-tournament favourites.
Harry Kane, Jude Bellingham, and Phil Foden were a shadow of the players who shone for their club sides last season.
Instead, England had to rely on a series of fightbacks and individual moments of brilliance to get past Slovakia, Switzerland, and the Netherlands in the knockout stages.
Spain, though, were a class apart as La Roja got the reward they deserved for being the best team in the tournament throughout.
“They are the best team in the tournament and they were the best team tonight,” added Southgate.
“Our players have been incredible, they’ve given everybody some incredible nights. They couldn’t have given any more in terms of their effort, their desire, their character. Tonight we fell short, we didn’t keep the ball well enough.”
Southgate bemoaned a number of physical issues as a laboured Kane was substituted for the fifth time in the tournament. His team also had one day less to prepare than Spain, who won their semifinal against France on Tuesday.
But the England boss acknowledged that Spain’s dominance of possession had ground his side into submission.
“Ultimately we lost to the better side and we have to reflect on how that happened but it is very clear in my mind,” added Southgate.
“For me the key was position of the ball tonight and we didn’t have enough control.
“There was a lot stacked against us tonight in terms of having a day less to recover from the previous game and having had the extra time periods that we did. But we have to hold our hands up.”