England's dismal World Cup campaign, and the uninspiring friendly win over Norway last week, led some to question whether Hodgson was the right man to lead England forward.
But the critics were temporarily silenced on Monday night in Basel as England beat Switzerland in a game billed as their toughest in Group E.
"You're always under pressure," the England coach said.
"The day when an England manager is not under pressure, we're not asking enough of him and his team, so that's never bothered me."
Hodgson has always maintained England's early World Cup exit was down to "fine margins" rather than any dramatic collapse.
The England manager resisted the temptation to make wholesale changes in the wake of the disappointing campaign in Brazil and has maintained his trust in the youngsters he introduced towards the end of the last qualifying campaign.
"On Monday the players proved what I have been trying to say all along," Hodgson added.
"They proved that, yes the World Cup didn't go our way and we were very disappointed, but we have been building, we have been changing players, introducing new ones, so it wasn't a question of us suddenly hitting a brick wall (in Brazil). It wasn't a case of 'all of a sudden this is all wrong, we have to do something different'.
"It was a question of maintaining faith that we're on the right track, that we were getting the right players in the team.
"These young players will be good players without a shadow of a doubt so it was important to get off to a good start against the team in the group which people will be thinking are our biggest rivals."
Hodgson was also happy that his players maintained their desire to play for England despite the winless campaign in Brazil.
"The one thing about these players, and I hope the public understand this, is that they all have a burning desire to play for England," the 67-year-old added.
"Jack Wilshere would play left-back if I asked him to.
"That theory that players care more about their club sides is nonsense.
"They care about both. Ever since I encountered these players, there has not been one who has not really shown me that they want to play and do their best for me."
