The loss was the Three Lions' biggest home defeat since a 5-1 loss to Scotland in March 1928.
England are now bottom of their Nations League group with just two points and have failed to score a goal from open play in their four games so far.
The England fans at the Molineux Stadium made their frustrations known after the final whistle as they booed the team off but Southgate has taken the responsibility for the loss.
"We picked a young team with energy, and when the game started to go against them it started to look that way [that it was a young team], and that's my responsibility in the end," Southgate told Channel 4.
"I felt at half-time we needed to go for the game, we made changes that gave us a bit more attacking impetus but then we were more open as well, and in the end you're pushing with so many attacking players, that left us wide open.
"I just said to the players there, across the four matches that's my responsibility. I tried to balance looking at new players, tried to rest players, we couldn't keep flogging our more experienced and better players, and in the end the teams I've selected haven't been strong enough to get the results in the two Hungary games really.
"I think the other two performances [against Italy and Germany] have been more positive than perhaps the reaction to them, but I understand tonight is a chastening experience."
Asked if he understood the flak directed towards him, Southgate said: "Of course, in the end this is about winning matches with England, tonight was a night like many of my predecessors have had and experienced, and it's difficult to stand here… I'm not going to say it doesn't hurt, but it's very clear to me what we're trying to do across these four matches.
"The irony is, the two Nations League campaigns are arguably the ones that have heaped negativity and pressure on to us, and you wouldn't normally have that [the Nations League] as an England manager.
"I've got to go with that. I've got to protect the players. They've been exceptional in their attitude, they've never stopped. The results are my responsibility."
