That is according to skipper Harry Kane, who admitted they were not good enough on the night.
The Three Lions lost their final friendly before Euro 2024, which gets underway at the end of this week.
"Of course there will be some noise about it (losing to Iceland) but I think there is a lot of optimism from the fans and rightly so," Kane stated to reporters.
"Ultimately it is down to us to make sure we get it right on the pitch.
"This could be a nice wake-up call for everyone to realize it is not going to be as easy as people think. There is a lot of work to do."
"I think there are some things we have to improve, for sure," he added.
"It was one of those games. On another day we had three or four clear-cut chances - myself, Cole, Ant had a good chance - so we could have walked off at 3-1 or 4-1 and we would all be going into the Euros very happy."