The Three Lions exited Euro 2016 at the last-16 stage in humiliating fashion in June as they were beaten 2-1 - the score from the 18th minute - by Iceland, after which boss Hodgson promptly resigned.
England have since opened their World Cup 2018 qualifying campaign with a 1-0 win in Slovakia overseen by Hodgson's replacement Sam Allardyce, who then left the job after secretly filmed footage of him making controversial remarks was released by the Daily Telegraph.
Gareth Southgate has subsequently taken over as interim boss, with his first match in charge coming on Saturday when Malta visit Wembley in England's second Group F fixture.
And when asked ahead of that clash about lessons learned from the Iceland debacle, Tottenham right-back Walker said: "I just think we don't need to play into their game.
"I thought probably in the summer, that's what we did and we didn't really have a different plan.
"It was 'we are going to play this way', and if it didn't work, then we didn't really know what to do.
"But I feel for the Malta game we have different dimensions now. We have spoken about it in depth - that if something is not working, we need to go to this plan."
England manager contenders
England manager contenders
1/6 Gareth Southgate - 6/4
Highly thought of by the decision-makers at the Football Association, the former Middlesbrough boss was brought into the fold to coach the Under-21s with an eye on future progression. Faltered at last year's Under-21 European Championship but led the team to victory at the Toulon tournament in the summer. Had no interest in succeeding Hodgson but takes charge for England's next four matches against Malta, Slovenia, Scotland and Spain while the FA looks for a permanent appointment.
2/6 Steve Bruce - 2/1
The former Manchester United defender was interviewed in the summer about the vacant England manager's job. Just days after speaking to the FA, Bruce decided to call time on his spell at Hull, where he had become the most successful manager in the club's history. He remains out of work.
3/6 Eddie Howe - 8/1
A smart, erudite and tactically-savvy coach who, at 38, looks to have a bright future at the top of the game. The manager has flourished at Bournemouth and only last week described coaching England as the "ultimate" job. "I would never say no," Howe said.
4/6 Alan Pardew - 8/1
Seemed to be a new man after swapping Newcastle for Crystal Palace and some fine early-season results saw him seriously linked with the England job for the first time in his career. Reached the FA Cup final but league results tailed off badly. A slow start to this campaign has been followed by three successive Premier League victories.
5/6 Jurgen Klinsmann - 10/1
The former Tottenham striker has managerial experience at international level, having been in charge of the United States for almost five years and Germany before that. America fell to a semi-final Copa America exit in the summer while Klinsmann guided Germany to the last-four stage at the 2006 World Cup.
6/6 Gary Neville - 25/1
Seemed a heavy favourite to progress from his role as Hodgson's assistant until his ill-advised stint with Valencia saw his stock plummet. It may yet be decided that was a case of the wrong job but the right man. Out of coaching since exiting with Hodgson during the summer, the videos of Allardyce appear to show him saying Neville was the "wrong influence" on his predecessor.
In the build-up to the summer's tournament, England midfielder Eric Dier - Walker's team-mate at Spurs as well - had emphasised the importance of the side being "streetwise".
That echoed the sentiments of captain Wayne Rooney as Hodgson's men crashed out in the group stages of the 2014 World Cup - and Walker has now made use of the word himself.
"I think the quality in the dressing room is frightening," Walker, 26, said of the England camp.
"And I think as soon as we just start gelling together and being a bit more - Eric Dier said it - streetwise, it will be a lot more beneficial for England and for us as a group of players."
One man Walker feels has already shown that in his game is another colleague for both club and country, midfielder Dele Alli.
After winning the PFA Young Player of the Year award last term - as Walker did in 2011-12 - in a fine season with Tottenham, then having a disappointing summer with England, Alli has recently started to find form again.
Walker said of the 20-year-old: "I think it's a vital year for him.
"I remember when I got the award - to follow it up the next season is what makes you a good player.
"He's doing it tremendously well. He deals with the weight on his shoulders, taking it in his stride.
"He is an intelligent boy - he is, as we said before, streetwise. I always say he looks like he is playing in the park.
"I think he needs to keep it simple sometimes, which the manager does tell him. But when he does express himself in the final third, you can't have a go, because more times than not it does come off."
Walker, Dier and Alli were among five Spurs players in the England squad at Euro 2016, along with Harry Kane and Danny Rose.
Walker ranks their embarrassing exit as the "lowest moment" of his career, and says Tottenham boss Mauricio Pochettino - whose side are currently second in the Premier League - was key in the quintet moving on from that disappointment.
"I got a short break and spent some time with my family, and it kind of takes a little bit of the pain away," Walker said.
"But it was still in the back of my mind when I got back to Tottenham and the gaffer put his arm around us all and we had a little chat. I think it was a good learning curve for us.
"We pulled together as well. We are a very close bunch of lads."