A dreary Nations League encounter in Reykjavik came to life late on, starting with Walker picking up a second yellow card for a rash challenge that left England down to 10 men.
Raheem Sterling converted a stoppage-time penalty for the visitors to give them a late lead, but Joe Gomez immediately conceded a penalty to give Iceland a chance to level.
However, Birkir Bjarnason blazed his spot-kick over the bar and England held on.
Walker accepted responsibility for his mistake following the game, with the 30-year-old admitting his international career does not have many games remaining.
"To get sent off for your country is never a nice moment especially after being out of the team for so long and being on 49 caps," Walker told Sky Sports.
"I have to take the full blame. To make a rash challenge like that is not acceptable. I don't blame the pressure, I am a seasoned professional and I should know how to manage a game.
"You have to say fair play to the lads for digging in and fighting and getting the win.
"The first couple of games back were always going to be tough. We have a good bond here, a great spirit. Maybe it was why I got the red card, I want to leave everything on the pitch for everyone.
"It is brilliant for English football seeing the youngsters coming through. They are proving it at the big clubs. The world is their oyster. That is the sad thing about being a footballer, it comes to an end sometime and I am probably nearing the end of my international career.
"Hopefully I will be back. I have to talk to the boss and see what he wants to do. I am more than happy to say I want to be around the team. I have missed it."
England manager Gareth Southgate concurred with Walker's assessment of his card, saying the Manchester City man has to better control himself.
"The sending off was a key moment and it is very difficult to win any game when you are down to 10 men. It's a lesson we have to learn and it was an unnecessary red card," Southgate told Sky Sports.
"We get the penalty and Raheem's drive and desire was outstanding and then there's another lesson we have to learn. We conceded a penalty, we got away with it and we leave with a win that is really important. It's a bit flat because it feels we got away with it.
"Kyle Walker realises, as an experienced player, those sort of challenges invite the opportunity for a referee to make that decision.
"We have talked a lot over the years about discipline and the amount of time we have gone out in tournaments when that has been critical — it is not what we want to see again."