However, the first of the Seattle bands which made up the grunge music scene - a fusion of punk, indie and rock - Soundgarden, released their most successful album, Superunknown, that year.
The Grammy-winning album produced the hit singles Black Hole Sun and Spoonman, and helped the band achieve worldwide sales of more than 20 million records.
The re-mastered digital version of the album will be released this year to mark its 20th anniversary of release. The group, which reformed in 2010 after a 13-year hiatus, also played the album in its entirety for the first time at the iTunes festival in Austin, Texas, last month.
"We were touring at the time of Kurt's death," lead singer Chris Cornell recalls, "and we just came off stage to be told of the reports that they had found Kurt, and he was dead.
"We were very emotional. All of the bands in Seattle had grown up together, we were all friends. I wanted to deny it, I didn't want to believe it was true. It was one of the most difficult things I've ever had to hear."
Guitarist Kim Thayil adds: "In some ways, I agree, grunge was already coming to an end at the time of Kurt's death.
"Sure, we released Superunknown that year, but all of us, the successful grunge bands, had left Seattle and were endlessly on the road. In the meantime the city was full of musicians moving there, wanting to make it in the industry. It was like LA during the '80s, the Sunset strip and hair metal. It had lost its vibe."
In the past, Cornell has described Soundgarden, who formed in 1984, as "the band that created the soundtrack" for grunge music.
Out of all the groups that formed in Seattle in the late 1980s - most famously, Nirvana, Pearl Jam, Alice in Chains and Mudhoney - they were the first to sign to a mainstream label. But it was the release of Nirvana's Nevermind album, in September 1991, which put the city, and its then-unique style of music, on the musical map.
"I don't think there ever can be those conditions in the industry again to produce something like the Seattle band scene, of which Nirvana were the cultural event," he says.
"Seattle was an isolated and provincial place that was left alone for years to develop its musical scene. None of us had overnight success, it's not like suddenly one day Nirvana, Soundgarden and Pearl Jam all formed.
"It all changed after Nevermind, it became commercialised. Everyone wanted to discover the next big thing."
"I don't think the grunge movement was actually original," continues Thayil.
"It was just a a synthesis of different underground music genres. What made it original was the kind of people doing it - it was our extreme youth. I think most of us were trying to fit in with the rock scene in the city, but because we were also fans of darker music - British bands like Joy Division, Killing Joke, Bauhaus, The Smiths - our shows reached a whole other audience of kids.
"All of us in these bands were influencing each other, I think that was our secret to developing the sound. We were all watching what the other bands were doing, there was a real friendly rivalry between us all.
"We all borrowed from Nirvana, but they also borrowed from us. It became something electric in Seattle and it felt great to be influential for a moment in time."
Soundgarden drummer Matt Cameron agrees: "The success of Nevermind took everyone by surprise."
"Of course, Kurt was a very special frontman, anyone could see the rapport between him and his audience - but no-one could ever have predicted that album would sell 30 million copies.
"And again, this couldn't happen again in the digital age because kids would already have been file sharing, but also, social media would have built a hype. What happened with the grunge movement was organic, and I wonder if that will be the last time that can happen in the music industry.
"Certainly I'm not sure there'll ever be a regional music movement again, and I don't think the next big thing in music will involve guitars - right now rock has lost its place at the centre of music."
After Soundgarden's split, Chris Cornell went on to form supergroup Audioslave, with members of Rage Against the Machine. Soundgarden's reformation in 2010 led to the hit album King Animal in 2012, but they have returned, Matt Cameron insists, to "a different world".
"Think about it," he says. "We've been invited to something called the iTunes festival, which is one of the biggest brands in music, and didn't exist before, and Lady Gaga is hanging around Austin, Texas, at what was once a little event for alternative music called SXSW. Our concert is being streamed live to millions of people, it's a strange concept to us. But it's humbling to have produced one album at least that still resonates after two decades.
"We released Superunknown a month before Kurt's death. You know, if you were part of the Seattle scene you were soldiers in the field. We enjoyed a lot of success but we all lost a lot too, and Kurt is the biggest example of that. Those of us who are left are friends for life.
"Dave Grohl is a great friend of ours still, he directed a recent music video for us, and he's turning into a very talented filmmaker too."
It's the loss of the talent of Kurt Cobain that Chris Cornell argues is the most difficult to deal with.
"To have all that promise snatched away, to think of all the things he could have been creating now. The possibilities were just so great."
The re-mastered edition of Superunknown by Soundgarden will be released in the UK in June 2014.
The death of Nirvana frontman Kurt Cobain on 5 April 1994 in Seattle, Washington, has sometimes been described as the event that marked "the end of grunge".