On Wednesday the England squad touched down on home soil following their worst ever display on the world stage.
Hodgson's men became the first England side since 1958 to exit at the group stage and secured just one point from their three matches.
That came from an uninspiring 0-0 draw with Costa Rica - a result which typified a World Cup performance that left defender Jones ashamed.
"It's not good enough," he said. "We know that. We can't say any more about that now.
"We just have to look forward and there are some positives and there are some negatives as well, but we have to go forward and go home and reflect on what has been probably a tournament to forget.
"We created chances all through the tournament. I know they say you create your own luck.
"At times we were unlucky. It's not an excuse, we can't rely on decisions like that. Like I said we will go away and reflect on it and look where we could have done better."
The inquest into England's failings is already well under way, although Jones refrained from wading in on the debate.
The defender said this is "not the time to be shouting our mouths off", although was quick to defend manager Hodgson, who has naturally come under-fire for failing to win in Brazil.
"Roy, the boss, has been terrific," Jones said. "Every training session he has put on the lads have responded to it. We can't thank him enough.
"It's us players who go out on the pitch and ultimately do the business and we have fallen short of that."
This is now a time to "regroup and push on again" in Jones' view, with the upcoming European Championship qualifying campaign offering a chances to right some wrongs with the young talent that impressed in Brazil.
"The clear positives are the young lads who have come through, likes of Luke, Raheem, Ross," Jones said.
"Luke and Ross today were really good. Raheem has been terrific through the tournament, I thought.
"He is dangerous, he is quick and he scores goals. No matter what people say the future is bright but it is difficult for people to see that now."
As for Jones, he wants to secure a regular place in the starting line-up for country and club.
"I would like to go back to the club and cement a regular place," the versatile Manchester United man added.
"I have said in the past few years that sometimes it doesn't really affect me but it is nice to cement a regular place. Hopefully I can do that.
"You have seen me play centre-back, right-back and the holding role in midfield. Obviously I think I am an out-and-out defender.
"I say it every week I am happy to play anywhere for the Manchester United. That is for the manager to decide."
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