In what was billed as a farewell game under the Wembley arch, England's players trudged off having applauded a half-empty stadium following an early exodus and jeers at full-time.

Iceland took a shock lead through Jon Dagur Thorsteinsson's early effort and the visitors then had the better chances to extend their advantage as the hosts toiled at both ends of the pitch.

It was not ideal preparation for one of the tournament favourites in Germany and England skipper Kane knows lessons have to be learnt ahead of their Group C opener against Serbia next Sunday.

"I think there are some things we have to improve, for sure," the Bayern Munich striker said.

"It is one of those games. On another day we had three or four clear-cut chances - myself, Cole (Palmer), Ant (Gordon) 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.

"But sometimes you need this wake-up call. There are areas we need to improve, especially with our pressure. The group games are going to be very similar to this. We are going to have to defend well, especially the longer balls, and with the ball we need to be a bit more patient.

"It is one to look back on. Obviously we have a couple of days with our families now, to have a little break, and then a good week building up to an important tournament in the summer.

"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. 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 realise it is not going to be as easy as people think. There is a lot of work to do."

England reached the final of Euro 2020 only to lose on penalties to Italy, while Kane's miss from the spot at the 2022 World Cup saw Gareth Southgate's side eliminated at the hands of France at the quarter-final stage.

"Yes, it was pretty s*** wasn't it?," Kane replied when asked if he thinks back to how the last tournament ended.

"I think in football you are going to have ups and downs on the way. Of course that was a down for me at the moment but I think over two years, for club and for country, I have put that to bed and I am just excited for another major tournament.

"Being so close in the last Euros, there is a real hunger to be back. It comes around quick, if I'm honest. We had the World Cup and we are back here again. I feel like we are on the right path. But as we all know as well, it is really difficult to win these tournaments.

"There are a lot of things that you have to do right and prepare right, and you need a bit of luck here and there. Every winner does.

"We have that mindset that we can achieve it. We also know there is a lot of hard work from now until the final in July."

Harry Kane: Iceland defeat a necessary 'wake-up' call for England