Gold, who was his co-chairman and a lifelong Hammers fan, sadly passed away at the age of 86 in January following a short illness.
He took over the east London club alongside Sullivan in 2010, with the duo becoming joint chairmen following their takeover.
On Wednesday night, West Ham beat Fiorentina 2-1 to win the Europa Conference League, their first trophy since the FA Cup in 1980.
Sullivan was in attendance for the game in Prague and expressed his sadness to have not shared the celebrations with Gold.
On the following morning, he delivered a lovely tribute to his former business partner and Gold's daughter Jacqueline, who also sadly died this year.
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Speaking to talkSPORT Breakfast, he said: "Absolutely elated, I'm so pleased for the supporters.
"The only great sadness for me is that my long-term business partner David Gold and his daughter, lovely Jacqueline, were not there to celebrate it.
"In life you only have so many football seasons, and the seasons ran out for him, you know.
"I'm lucky enough that one of my seasons we actually won something, the manager is exactly the same, you get so many football seasons, he's never won anything, but he won something big last night.
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"I looked up a couple of times, I pray for David Gold every night to the heavens. I know it sounds corny but every night since he's died I've prayed to the heavens.
"I do believe there's someone who does look down on you sometimes and gives you a bit of good. I've been praying for winning this game for weeks and thankfully we did."
Sullivan also confirmed that the Wednesday night's win was Declan Rice's last game for West Ham ahead of the summer window.
As captain, he lifted the trophy in Prague and has therefore capped off a wonderful spell at the club with silverware.