The boss of the Three Lions praised his team's display against Les Bleus, despite failing to hang on to their one-goal lead
The former West Brom boss praised his team's discipline and work rate as they battled to earn a point against a talented Les Bleus team.
The 64-year-old was happy with the end result, despite England taking the lead through a Joleon Lescott header midway through the first half, with Samir Nasri equalising for Laurent Blanc's side, with a powerful low shot from outside the box.
Hodgson speaking to ITV after the game said: "For me, it was a very good team performance. Everybody did their very best to keep us in the game. We defended properly and we attacked properly.
"I think we played well, we played against a top team, they do ask questions of you, they're very patient, they've got a lot of talented players, when they get the ball in your final third they don't panic."
"You have to very disciplined in your defending, to get a 1-1 draw and ask the questions of them that we did, you have to be quite happy."
The veteran manager went on to admit he was not too concerned about relinquishing a 1-0 lead so soon, when Nasri's effort beat Joe Hart to put France level.
"I don't know about frustration, the fact is they are a good team, taking the lead is one thing, it doesn't mean your opponents are never going to get the chance to score a goal.
"We kept them very much at bay, there wasn't that many situations in front of our goal where I was panicking in any way.
"We had quite a few situations in their part of the field where with a little bit more luck with the final ball we could have got a second goal.
"The final ball, decision making in the final third, sometimes we were a bit too anxious when we got there, or we crossed too early, we don't get the right type of cross, or we try a one touch pass when we should have taken an extra touch, but it's all a good sign of players wanting to do well."
The England manager also had words of encouragement for Alex Oxlade-Chamberlain, who made his competitive debut for the national side.
"I thought he did quite well, I thought he was quite dangerous. A couple of times he got brought down on a very good run, had that run been able to continue, who knows he might have been able to create something."
Hodgson was also happy with the performance of the referee, despite several decisions not going England's way during the match.
"The referee did okay, it's foolish to start commenting on referee's performances, sometimes you get a little bit of luck on your side sometimes not.
"I know Steven [Gerrard] was a bit aggrieved not to get the free kick, but to be fair there was a couple of them where players go down, but he was fair to both sides, it wasn't a one sided performance."
With France being labelled as England's toughest opponent in the group stage, the former Liverpool boss declined to underestimate the other teams in the group.
"France are one of the favourites, no question of that. Twenty-one games before this unbeaten, everyone tipping them to be a potential winner of the tournament, so we can't deny on paper that it may have been the hardest game, but I have a lot of respect for Sweden and a lot of respect for Ukraine.
"[I'm] very proud of their performance, I didn’t think there was any player on the field who let us down. I didn't know what the result would be, I didn't know how well we'd play, but I was pretty confident the players would not let us down."