"None of us is satisfied with two semi-final appearances in successive years," Southgate told reporters. "We all wanted to move forward further.
"We needed to finish what's been a good year with the international team with a strong performance."
Southgate said it was a good thing that the players were feeling they could have achieved more.
"We owed it to ourselves... The commitment is there. They're not satisfied with where they're at and that, as a coach, gives you a lift," he added.
Southgate also voiced his displeasure over UEFA's decision not to award England their bronze medals on the field after the game.
"We've had to go through another third/fourth-place playoff and have finally won one, and we don't even get the medals in front of our fans," Southgate said.
"It's nice to have some acknowledgement, but we'll be parking it to one side and looking forward."
(Reporting by Shubham Kalia in Bengaluru; Editing by Peter Rutherford)
