Midfielder Coke clinched maximum points for the Owls with a tremendous left-footed shot into the top corner four minutes before the interval.
Brighton were forced to play the final 40 minutes with 10 men after midfielder Andrew Crofts received a straight red card for a high tackle on Sam Hutchinson, but Gray felt his men fully deserved their win.
It took Wednesday 17 games to record their first victory last term, and Gray said: "It's good to get that monkey off our back straight away.
"It was an overall team performance and every player put in a eight or nine out of 10 display.
"(Brighton manager) Sami (Hyypia) will be disappointed, but we controlled the game and deserved the three points."
Gray felt the dismissal of Crofts was the correct decision based on the amount on contact there was on defender Hutchinson.
He explained: "The referee did a very good job and took his time. If Sam stays down, it was the right decision."
Gray, who has boosted his threadbare strike force by bringing in St Johnstone striker Stevie May for about £800,000, was full of praise for the 2,500 travelling fans and is eager for his men to build on their good start.
He added: "We had unbelievable backing and we won the game with a stunning goal.
"The division will be wide open and I'm delighted with my team; it shows what team spirit and determination can do."
Brighton boss Hyypia was especially disappointed to lose his first managerial game in England, but warned it is far too early to judge his men as the squad is not up to strength yet.
The former Liverpool defender, who is demanding that the Seagulls work hard at all times, refused to blame the dismissal of Crofts for his side's opening day loss.
The Finn said: "I saw what I saw. I don't want to look at it again as I can't change the decision. (The referee) made his decision and we lost the game.
"I liked the effort of everyone on the pitch, although the red card didn't make it easier.
"There are 46 games in the Championship and I'm not happy we lost as every match is very important."
Brighton chairman Tony Bloom has reassured fans they will be happy with the squad by the end of the transfer window, and Hyypia says the Seagulls are working hard to bring in their targets.
He added: "We have our targets and we need to get them in as soon as we can.
"We need to work hard every day and teach the players to make the right decisions; we are working on things every day.
"We played okay today and are on the right path: it's work, work, work.
"It's nice to come back to football but there's not a lot of time for a breather. Football is a big part of my life and I want to do this job and I want to improve and develop myself."