The highs of qualifying for Brazil with wins over Montenegro and Poland last month were replaced with jeers from the home crowd after a first-half header from Arsenal centre-back Per Mertesacker proved enough to give a much-changed German side a 1-0 victory at Wembley on Tuesday night.
Hodgson has some seven months, of course, to get things right before the action starts for real in Brazil next summer.
Jagielka feels some important lessons can be taken from what has been a sobering spell for the Three Lions following the euphoria of October's success.
"They are a South American team, they have a certain way of playing and you hope to pick up a few bits and bobs which potentially you might come across in Brazil.
"Against Germany, it was difficult to learn too much because they made a lot of changes to their starting XI and we made a lot during the game, but on the counter attack, we have come up against a very special team making some fantastic runs and that is something we will have to take a look into."
Hodgson looked at 25 players during the losses to Germany and Chile, with Southampton duo Jay Rodriguez and Adam Lallana making their senior debuts, along with Celtic goalkeeper Fraser Forster.
Liverpool midfielder Jordan Henderson and Arsenal left-back Kieran Gibbs returned to the international fold after a long absence, while Ross Barkley and Tom Cleverley were given a chance to prove they are worthy of a ticket to Brazil.
By the time England meet up again for their friendly against Denmark in March, Hodgson will have named his provisionally 30-man England squad for the World Cup.
Everton centre-back Jagielka, 31, knows that is when the real hard work will begin as attention sharpens towards next summer.
"We are still a work in progress and it is all about progression," he added.
"We have some more friendlies coming up before the World Cup, and we know what we need to do to improve."