Hodgson avoided becoming the first England manager in history to lose three successive home games as Daniel Sturridge's late header saw off the Danes.
But Italy coach Cesare Prandelli will hardly be quaking in his boots when he sees the replay of the first 45 minutes.
Whether he meant it a slight at the home nation or not - Denmark coach Morten Olsen summed up England's predicament perfectly when he stepped away from his post-match press conference and said: "Good luck at the World Cup. You'll need it."
Still, Hodgson, as ever, was at pains to pick out the plus points from the victory, which came in front of just over 68,000 fans.
"The victory was positive," the England manager said.
"We thought in the first half we passed the ball neatly enough, but not with the tempo we were looking for.
"But we put that right in the second half. We got in so many crosses, some a hair's breath from going in or creating a chance. "That's positive. This was never an easy game. Denmark are no mugs and know how to play football, so it's nice to go away with this victory before we meet up in May when the next matches are preparation."
Denmark are not "mugs" but they are hardly on a par with some of the teams England could run into at the World Cup.
To point out the task that could be in hand for the Three Lions in Brazil one has only to look at Spain's bench for their 1-0 win against Italy on Wednesday.
Alvaro Negredo, Xavi, Xabi Alonso, Jesus Navas, David Silva, Victor Valdes and Santi Cazorla were on the bench in Madrid. Juan Mata and Fernando Torres were not good enough to make the squad.
England did not have experienced stars from top European leagues to call upon.
Instead, Wednesday night's World Cup audition night belonged to Raheem Sterling plus second-half substitutes Adam Lallana and Luke Shaw.
Sterling's fancy footwork almost brought him a maiden England goal - he hit a post in the second half and earned the man of the match award - while Lallana's trickery gave the Three Lions more flair.
Hodgson says his task of picking 23 players to go to Brazil is now much harder.
"Shaw and Lallana were very good," Hodgson said.
"You couldn't get me to say anything negative about any of the young players.
"They did a good job and improved their chances."
England improved on their dull first half after the interval and had it not been for Kasper Schmeichel's athletic saves, this could have been a much more straightforward win.
Joe Hart was rarely called upon thanks to Denmark's reluctance to get forward, although he had to be at his best to deny Morten Rasmussen in the second half.
Hodgson now goes away for two months to consider his options. He insists he has more players to consider than he did last summer when England were at a low ebb versus Republic of Ireland.
Twelve months ago Luke Shaw would have been considered a big outsider for the World Cup, but he did not pass up on the chance to impress on his debut, linking well with his Saints team-mate Lallana after his second-half introduction.
That said, Cole, the 107-cap veteran, also performed well, which leaves the England manager with a very tough decision to make on who joins Leighton Baines in the squad for South America.
"I thought Ashley and Luke were both very good," the 66-year-old said.
"It's (a) tougher (decision for me) now, yes, but there's a lot of matches still to be played.
"I'll see a lot of Luke Shaw, Leighton Baines and hopefully Ashley Cole in the coming months.
"I wasn't surprised with Ashley. I'm a great admirer of him.
"I've watched him in training and he's been unbelievably good, and very fit - right at the top of the running statistics - so there's no question about his fitness.
"But he's a specialist player. You don't normally play two left-backs in the team and, at the moment, his manager at club level prefers someone else."