The Hatters captain, 28, was taken straight to hospital, where he was pictured celebrating in his bed after his team-mates won a penalty shootout.
Clark told Sky Sports: “The gaffer said we had to do it for him.”
Edwards said it “felt a little bit wrong to celebrate”.
Luton were a non-league team just nine years ago, and their victory over Coventry took them back into the top division for the first time since 1992.
But the day had begun in worrying fashion as they lost Lockyer in just the eighth minute – the Wales international falling to the turf and having to be taken off on a stretcher.
Lockyer later posted an update on Instagram on his condition to say he was “feeling myself very much, helped by the way the lads left it all out on pitch”.
He was staying in hospital overnight as a precaution and would have further tests on Sunday, he said.
“I would just like to say a massive thank you to the amazing physios and doctors at Luton and Wembley for the swift and thorough response,” he added.
“A much scarier moment for everyone else than myself, I am sure!”
Despite losing their captain, the Hatters went in front through Clark’s first-half strike, but Coventry forced extra time when Gustavo Hamer equalized on 66 minutes.
Neither team could find a way through in extra time before a high-quality shootout ended with Coventry’s Fankaty Dabo shooting over.
Speaking soon after victory was secured, Edwards told BBC Three Counties Radio he was “only thinking about Lockyer”. He later told Sky Sports: “I just felt emotional. I feel for ‘Locks’, who has been our best player this year.”
Dan Potts, who wore the captain’s armband as he scored Luton’s sixth penalty, said he was “gutted” for Lockyer.
“He deserved to be there holding that trophy,” he added.
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