"Today is a very dark day, one of my worst as a coach," Huetter told Sky.
Frankfurt, who are challenging for a top four spot in the Bundesliga and held Chelsea to a 1-1 draw at home last week, were stunned in a bizarre first half at the BayArena where all seven goals were scored.
"We knew Frankfurt had an intense Europa League game behind them, so we wanted to play with energy from the beginning," Leverkusen striker Kevin Volland told Sky.
Kai Havertz opened the scoring for Leverkusen after just two minutes, and Julian Brandt added another before Jonathan Tah deflected in a Filip Kostic shot to briefly allow Frankfurt back into the game.
A brace from Lucas Alario, a Charles Aranguiz strike and a Martin Hinteregger own goal put Leverkusen 6-1 up by the 36th minute and completed a Bundesliga record of seven goals in the first half.
Frankfurt remain in fourth but are now level on points with Leverkusen, and only three points ahead of seventh-place Hoffenheim.
"I am not going to kick my team when they are down, we need to get the boys back on track," said Huetter.
Sunday's horror show also damaged what had been a healthy goal difference advantage over their rivals in the race for Europe.
- Schalke safe -
Elsewhere, Schalke secured their Bundesliga survival with a 0-0 draw at home to Augsburg.
"It's a shame for the fans that we weren't able to win today, but staying up was the main thing," said interim coach Huub Stevens.
Stevens, who had twice managed the club before and led them to UEFA Cup glory in 1997, stepped in and took the reins from Domenico Tedesco in March with Schalke just four points clear of the bottom three.
Sunday's draw put them seven points clear of Stuttgart, who are in the relegation play-off place, sealing safety with two games to spare.
Stevens refused to answer questions about former Huddersfield coach David Wagner, who played under him at Schalke in the 1990s and is rumoured to be next in line for the head coach job.
"As a member of the Schalke board, I am unable to comment," he said.
Freiburg also avoided the drop as they were held to a 1-1 draw at home to Fortuna Duesseldorf.
Vincenzo Grifo gave the hosts an early lead from the penalty spot, before Dawid Kownacki smashed in the equaliser for Duesseldorf on the half-hour mark.
Freiburg's Janik Haberer was sent off in the second half, but they held on to secure the point and another year in the top flight.