Danny Welbeck's second-half brace saw England make a winning start to their Euro 2016 qualifying campaign.
Hodgson had been under pressure after his side's poor World Cup and unconvincing 1-0 friendly win over Norway on Wednesday.
Speaking at a news conference after Monday's win, Hodgson said he always believed the midfield diamond would suit his team.
"We thought this could be a good system for our players," he said.
"I have said many times recently that the six players I have got in front of the back four, there is enormous potential in them.
"They have got youth, energy, talent and they can play in different positions so Sterling can play wide and central."
Raheem Sterling, Jack Wilshere, Jordan Henderson and Fabian Delph started in the diamond, with Welbeck and captain Wayne Rooney up front.
Hodgson said his players needed to embrace the responsibility of representing England, while he praised Rooney for his performance.
"Wayne learnt it long ago and if you are going to have a big career as an England player you have to take the responsibility and it comes with criticism and enormous scrutiny," Hodgson said.
"I am just pleased that some of the criticism of Wayne of late, at a time when he has been anxious to show how good he is and how much he wants to do this job, I was delighted tonight he could marry the two things together.
"There has never been any doubt for me in the games where he has been criticised that he has not been doing the absolute maximum.
"[It was the] best he can do but forwards play small margins and if a few passes go astray or a few goals chances get missed that is when the criticism lands on you and it was nice tonight to see him do that."
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