Capello has been wading back into choppy England waters again over the past few days, having what Hodgson described as a "cheap" attack on Wayne Rooney over his performances for the national team.
Rooney was part of the England side ripped apart by the Germans in Bloemfontein two years ago, beaten 4-1 in a one-sided last-16 encounter.
Capello refused to acknowledge the severity of that defeat, preferring instead to concentrate on the wrongly disallowed Frank Lampard goal that would have levelled the match, rather than the fact his team were comprehensively outplayed.
Low certainly knew it - and he clearly has not forgotten.
When asked how it was that Germany tended to remain at major tournaments after England had gone home, his observations came with backing for Hodgson.
"I don't know why," he said. "It's hard to answer.
"The English were much better in this tournament than in 2010.
"When they played us then, they were a team who had a lot of problems.
"Roy Hodgson has brought order into the side and has done a great job.
"(At Euro 2012) they were a very well organised team.
"England will develop under him in the next few years and, in the next tournament, they'll play a better role than they did here and certainly than they did in 2010."
Those words will provide comfort both to Hodgson as he starts preparations ahead of this autumn's World Cup qualifying programme, but also the Football Association, who shocked most observers by choosing the 64-year-old ahead of overwhelming favourite Harry Redknapp.
Not that Low refrained from implied criticism of England's performance against Italy in Kiev on Sunday when, yet again, they failed to impose themselves on the international stage.
"We saw the game," said Low. "After 60 or 70 minutes Italy just got stronger and stronger and had more and more chances.
"In extra-time, Italy were dominant and England physically got weaker."
It seems fairly obvious Germany will not be allowing Andrea Pirlo the amount of space he got in Kiev.
Low may be a big admirer of the Juventus midfielder, but he intends Germany to take the initiative from him.
"Pirlo is not just a very good player, but the player who dictates the tactics and gives the team their ideas," said Low.
"He's the Italian player who directs the game.
"We have to disturb him, stop him playing, get in his way, and think of a way how we can do better than Italy in midfield.
"We have to dictate the tempo of the match upon the Italians.
"I think we'll be able to do that."
Interestingly, influential midfielder Bastian Schweinsteiger, who has recovered from an ankle injury, revealed that Germany have not practised penalties.
However, as Hodgson argued the best way of avoiding that lottery is to get better at the actual matches, he would presumably be impressed at Germany's present world record run of 15 successive victories in competitive games - a run that dates back to their third-place play-off win over Uruguay.
It provides Germany with the confidence required to dismiss their awful record against Italy in tournament games, three defeats and four draws, most recently the 2006 World Cup semi-final when there were beaten by two goals in the final minute of extra-time.
"I personally don't have any 'fear'," said Schweinsteiger.
"Respect is there. Respect for what they've done in the last two years, and given the scandals in their league, their national team is really positive.
"If you don't have any respect you're dumb.
"Italy are a great nation, have won a lot in the past and have made a big step forward in the last two years.
"The point has come now, though, where we can beat the next big opponent.
"We've beaten Argentina, Brazil, England and Holland. The next one, we hope, will be the Italians."