He is correct, though - you cannot keep on harking back to what happened with Iceland. The loss was terrible but you also have to remember that that England team was also terrible. Our midfield consisted of Rooney, Dier and Ali. Two of them aren't even midfielders. Rooney was pretty much done by that point, to make things worse. Dier has never been a good player; average at best. Ali - I can't remember whether he was good or not at this point. Either way, it is a terrible team.
This team is far stronger and, despite all the praise Southgate is getting, we are actually repeating the results that we have had throughout the 2000s and 90s. It isn't any different; it is just that we are facing the better sides deeper in the tournament; the expanded Euros certainly increased the odds of having weaker draws. We benefited from that in the last tournament.
Southgate is a championship-level manager, at best. There are plenty of managers who could repeat what he has done, at the minimum. He hasn't done this 'fantastic job' that everyone is thinking he has done. He has beaten sides that England are expected to beat, but he has not been able to win a single game that is anywhere near 50-50. In the end, there is a point where you need to accept that we are not going to do it with Southgate, so give someone else a chance. He has shown over three tournaments he cannot win against these sides, so it is pointless going on with it.