An injury-time strike from Daniel Sturridge sealed the victory in Lens after Jamie Vardy had cancelled out a first-half free-kick from Gareth Bale.
England were denied a victory over Russia thanks to an equaliser from Vasili Berezutski just a few seconds before the final whistle in their opening game in Marseille, but Thursday's win has put them a point ahead of Wales and Slovakia at the top of the group with a game to play.
And Hodgson feels his side's performances in their two matches makes their position fully justified.
"I'd have been less ecstatic had we not conceded late on against Russia," he said. "It was always going to be important to win today and we thought we might if we put in a similar performance but the Welsh worked hard and restricted clear-cut chances.
"It took a lot of probing and effort but I was pleased to see both chances go in. Four points is the minimum we deserved from the two performances."
Vardy came off the bench to score the equaliser on his maiden appearance at a major tournament for England, who went on to win their first match at a showpiece competition while trailing at half-time.
And Hodgson was quick to compare the impact made by Vardy and team-mate Sturridge to that of Paul Pogba and Antoine Griezmann, who had helped France to a 2-0 win over Albania after starting among the substitutes for the hosts on Wednesday.
"He [Vardy] has a lot of confidence and I had no hesitation to put him on the field," Hodgson continued. "Harry Kane looked a bit tired so it was great to have him to step in, as well as Marcus Rashford and particularly Daniel Sturridge to ask some questions.
"I don't trust stats but it seemed we were on the ball so much, we had to make so many decisions on the ball and around the penalty area.
"Of the 23 players, the ones not selected will feel hard done by. I think it'll be a feature of the tournament, and watching France play Albania last night, it was similar when Pogba and Griezmann came on the field - they got the victory they looked like they might be denied."
Captain Wayne Rooney once again impressed in a midfield role and Hodgson believes the Manchester United man has vindicated his faith following some doubts over his pre-tournament form and fitness.
"It's not just his offensive qualities - it's nice to have a player like him in midfield as he is still a goalscorer," he added.
"But we're happy with the composure he brings, the calmness when it gets a bit frantic. His long cross-field passes have always been a feature of his game. In particular, having survived some of those doubts about him in the build-up to my selection, I'm pleased that he's shown he still has such an influence on the team."