Hodgson appeared in front of the cameras for the first time since the controversy that followed his half-time team talk against Poland last month.
The England manager told a joke to illustrate why his players should give the ball to winger Andros Townsend but was forced to apologise after claims it was racist.
The reporter who wrote the story claimed his source was a player inside the England dressing room.
Hodgson is still not sure if the leak came from among the playing staff and he has no doubts about any divisions within the ranks.
"There is certainly no question in my mind about unity and about our spirit," the England manager said.
"No-one has yet proved to me that it came from the dressing room.
"I am disappointed about (the story coming out), of course, but it is over as far as I am concerned.
"My thoughts are purely on these two matches and the World Cup matches ahead."
Hodgson insisted following the controversy that his comments were not racist in any way, and Townsend said he had no issue with the England manager over the matter.
The former Fulham manager does not feel the need to discuss the matter with his 28-man squad when they meet up at St George's Park on Tuesday, therefore.
The England boss looked a little tense as he addressed the media at Wembley on Thursday afternoon, though, and he concedes he may have to bite his tongue with certain phrases in the future in order to avoid the kind of headlines that marred England's qualification for the World Cup.
"Have I learned these days that something said so innocently can be so badly misconstrued and cause as much as pain as it did to so many people? Yes, I have learned that lesson," he said.
As a result of those two encouraging performances against Montenegro and Poland, England have, of course, booked their ticket to Brazil.
Now the planning for the competition starts in earnest.
That gives Joe Hart seven months to prove he still is the best goalkeeper in the land.
Hodgson has started all but two of Hodgson's 18 matches in charge, but the England boss confirmed that the out-of-form Manchester City man will make way for either Fraser Forster or John Ruddy for one of the two upcoming friendlies.
Hart has been benched by City after committing errors against Cardiff, Aston Villa and Bayern Munich, while he was also at fault for Scotland's opener at Wembley in August.
Hodgson insists he still has faith in Hart, who has been England's undisputed number one for the best part of the last three years, even though he will miss one of the games against Chile a week on Friday or Germany four days later.
"Joe will start one of two games,'' Hodgson said.
"But I don't think he'll start both.
"It's important for me to look at one of the other goalkeepers, possibly both.
"But I can say Joe will definitely start one of the games as he's our number one goalkeeper.
"I believe in Joe Hart.
"I would be a lot more concerned if in the spring of next year as we are building up to the selection if he was a constant reserve.
"That would bother me but I firmly believe that Joe is such a good goalkeeper that he will get back into the Manchester City team sooner or later."
Hodgson, who handed surprise call-ups to Southampton duo Adam Lallana and Jay Rodriguez, is sure either Forster or Ruddy, who have just 45 minutes' worth of international experience between them, are strong enough deputies.
"We admire Fraser Forster," Hodgson added.
"He is a good goalkeeper. I want to put a word in for John Ruddy as well, because I know he let (seven) goals in on Saturday (against Manchester City).
"I suppose in the moment that doesn't help his cause but before that he was getting some good reviews for Norwich and doing some good things."
Hodgson has recalled Jordan Henderson and Glen Johnson, but there was no place for highly rated youngsters Saido Berahino, Ravel Morrison or Luke Shaw.
The England medical team will assess Jack Wilshere's ankle injury before deciding whether he will join up with the squad on Tuesday.
Goalkeepers: Fraser Forster, Joe Hart, John Ruddy.
Defenders: Leighton Baines, Gary Cahill, Ashley Cole, Kieran Gibbs, Phil Jagielka, Glen Johnson, Phil Jones, Chris Smalling, Kyle Walker.
Midfielders: Ross Barkley, Michael Carrick, Tom Cleverley, Steven Gerrard, Jordan Henderson, Adam Lallana, Frank Lampard, James Milner, Andros Townsend, Jack Wilshere.
Forwards: Jermain Defoe, Rickie Lambert, Jay Rodriguez, Wayne Rooney, Daniel Sturridge, Daniel Welbeck.
- Sports & Recreation
- Andros Townsend
- Joe Hart
- Fraser Forster
- John Ruddy