"I have never seen such a terrible defeat," said Rummenigge, who spearheaded the German attack in the 1980s and is now a leading official at European champions Bayern Munich.
"This was a new Waterloo for us. What really disturbed me was that we seemed to give up halfway through the match."
The home fans delivered a stinging verdict on the defeat, with the players suffering a cacophony of whistles long before the end.
"After this catastrophe, we mustn't make the mistake of giving up and breaking apart. I'm sure that we will go on to qualify."
Liverpool midfielder Dietmar Hamann was left stunned at the manner of the team's collapse.
"We just fell apart and that shouldn't happen," he said. "We knew the English and their coach were good but we conceded goals at the worst times.
"There's no way that the English were four goals better than us."
And team-mate Jens Nowotny was equally non-plussed by the result: "It wasn't the fight we expected. Nothing worked for us."
Fellow defender Marko Rehmer said simply: "This is a pathetic result."
German coach Rudi Völller left the stadium minutes after the final whistle to be at the bedside of his father who had suffered a heart attack during the half-time interval.
In Völler's place, Germany's deputy coach Michael Skibbe said: "I could criticise the whole team's performance - we displayed weaknesses in defence and attack.
"We made just as good a start as England, but unfortunately we conceded two unnecessary goals in the first half.
"Until it went to 4-1 we kept up the pressure, but the game had got away from us by then."