Luton have struggled to find their feet in their first season in England's top flight since 1992, having won just one in 16 in the league, and not registered an away league win in 2024.
"We didn't get relegated because of today, it was a culmination of the whole season. Today was the difficult day but we've been on an incredible journey. I'm just really disappointed that I'm the one responsible," he told reporters.
Edwards praised his side's performance in the first half, where Luton went into the break 1-0 up thanks to a sixth-minute header from Belgian midfielder Albert Sambi Lokonga.
"We showed some really good things to go 1-0 up. We showed at times we've got quality to get behind them and get into good areas," he told reporters.
West Ham's quality proved too much for the Hatters in the second half, and a much-improved performance from the home side saw goals from James Ward-Prowse, Tomas Soucek and George Earthy dealt a hammer blow to Luton's hopes of survival.
"Credit to them, they've got some really good players and we came up short," Edwards added.
Luton were not officially relegated on Saturday after Nottingham Forest lost 3-2 to Chelsea, but it will take a final-day miracle for them to survive.
They host Fulham on the final day of the season needing to overcome a three-point and 12-goal-difference deficit to 17th-placed Forest, who visit already relegated Burnley.
Luton have won the respect of rival teams and fans alike this season with their style of play and approach, having risen all the way from the Conference - England's fifth tier - in the last 10 years to achieve a place in the Premier League for this season.
West Ham fans applauded Luton's players off the pitch at the end of the match, which Edwards said was "touching".
"At times I think we've shown that we can compete with loads of teams, with everybody, and the growth and the improvement, I take pride in that," he said.
"I've loved it, and it fuels the fire to get back in."
Luton have struggled to compete financially with other teams in the Premier League this year and have spent far less than any other club according to Transfermarkt.
"We got promoted with one of the smallest budgets. It was a huge gap, chasm, between us and the Premier League. That won't necessarily be the case now, we can be one of the stronger teams."
With Sheffield United and Burnley already relegated, it would be the first time since the 1997-1998 season that all three promoted teams go straight back down.
Edwards said they wanted to go out in style against Fulham on the final day.
"We want to try and go out on a high and show the best us, we owe that to our supporters, ourselves, and the league."
