Ferran Torres scored a hat-trick for Spain in Sevilla, leaving Loew to pick through the wreckage of Germany's worst defeat for 89 years.
"This has been a black day for us," admitted Loew after Germany's heaviest defeat since losing 6-0 to Austria in Berlin in 1931.
"We completely lost track of our plan after we went 1-0 down, which was deadly and the Spanish took their chances.
"Nothing worked, neither in defence nor attack.
"We left huge spaces, there was a lack of communication between the players."
The thrashing was double that of Loew's previous worst defeat as Germany coach when his side lost by 3-0 to both the Czech Republic in 2007 and to the Netherlands in 2018.
Coming two years after their 2018 World Cup debacle, when Germany failed to get out of their group, this is the biggest crisis of Loew's 14-year reign.
The 60-year-old, who led Germany to the 2014 World Cup title, insists he can still turn things around with seven months to go before the European championships kick off next June.
Germany face world champions France and reigning European champions Portugal in their group.
"Of course," Loew insisted when asked if he wants to stay on, with two years left on his German FA contract.
"It's our duty to look at this and ask what we can do better.
"We were second best in every department, it was a black day -- there is no way of dressing this up."