The Baggies are back in the top flight after two seasons away after drawing 2-2 with Queens Park Rangers on the final day of the season, while rivals Brentford lost to Barnsley and Fulham drew to Wigan.
Head coach Slaven Bilic guided Albion to the Premier League at the first time of asking, his side ultimately having done enough before the coronavirus struck in March, meaning the four-match winless run to end the campaign did not prove costly.
Skipper Livermore said: "We know what it meant to us as a club, not only to us as players but those who work in and around the stadium, physios who might lose their job if it didn't go to plan, dinner staff, all of them. It meant so much to all of them.
"The players knew that and it's just relief. It's been a long ride."
He added on the fans: "They are here with us, we know they are.
"Throughout the lockdown we've loved to interact with as many as we could and it was a real eye-opener of what it means at this football club and to this area."
Livermore believes that, in a season that spanned 11 months, Albion merited their automatic promotion spot.
"Credit to Brentford, since the break they've been fantastic," he said.
"We've played well since we've come back. We've done everything we can. Done everything right. We had 20 opportunities against Birmingham and couldn't score.
"Anyway, I think over the period of the season we deserved to go up. It's an honest group, we played some good football and the boys have done well, the manager's done well. It's fantastic all-round."
On-loan Sheffield United frontman Callum Robinson was recalled to the starting line-up and played a significant role in helping his side over the line, with a goal and assist for Grady Diangana.
Robinson said: "Obviously I've had to wait for my time since lockdown but I've come in to help the boys and I did that.
"I made it hard considering I missed a one-on-one but I got the boys over the line and I'm just happy I was involved in that. Obviously the lads have done it numerous times. I came in January and tried to do my best and help the boys achieve this."