The Young Lions arrived at the Ander Stadium in Olomouc for their final Group B game against Italy with their destiny in their own hands, but a 3-1 defeat left them bottom of the group table and heading home early.
It is the U21s’ third straight group-stage exit and raised questions about Southgate’s selections and his own position.
The former England international signed a contract extension until 2017 in January and has no intention of reneging on that deal.
“I’m contracted to stay on, I’d like to stay on,” Southgate said, when asked about his future. “In the end, it’s not my decision.
“But I think what we’ve done over two years has progressed the profile of the team, the style in which we’ve played.
“I think we’ve had some massive success stories in terms of individuals that have come through the programme. Even in this tournament one or two players that have come through have emerged from it.
“So I think people will look at all of that when they’re making that decision.”
Andrea Belotti and Marco Benassi scored in the 25th and 27th minute respectively to set Italy on their way to victory and leave Southgate devastated.
He told Sky Sports News HQ: “You can’t lose a game 3-1 and say ‘we wouldn’t have done anything differently’, but I don’t think there are many things that we have got wrong.
“I’m sure we will reflect on all of it and think about everything from the beginning of the preparation right the way through, but in the end matches are decided on the pitch and a two-minute period really has swung the whole tournament on its head for us.”
Southgate, whose side came into the tournament with a record of 15 wins from 16 games, also felt injuries to key players John Stones, who returned to the back four to face Italy, and Saido Berahino had hindered his side in the Czech Republic.
He also insisted their performance should not be compared with other disappointing displays by England in tournament football.
“I don’t think we can lump this group of players in this tournament in with everything else,” he said.
“Every tournament is individual and the reasons for not progressing are all varied. I don’t think it’s one thing.
“I think this tournament has rested on a couple of injury setbacks before the first game which didn’t help us and tonight on two minutes of football. And that’s football – to win tournaments in those key moments you have to finish your chances or make the right decisions to keep the ball out of the back of your net. And in simplistic terms that’s the bit that we have fallen short on tonight.”
Captain and goalkeeper Jack Butland added: “Everyone will look to these kind of tournaments and expect us to do well, as they should. We expected to do well; we expected to do better than we did tonight.
“As hard as it is you have got to learn from these experiences. There’s so much ability in this squad, young players that have come in and players that have got years and years of top football ahead of them, and I just hope that they learn from this experience, learn what it takes to win on the big stage.”