Luton learned valuable lessons to secure first Premier League win
Having earned their first point with a draw against Wolverhampton Wanderers last week, they held on to take all three against the Toffees thanks to two first-half goals from set pieces by Tom Lockyer and Carlton Morris.
"We've been improving in every single game, and if people care to look at us in the first game and follow us over the next few they'll see improvement in every one," Edwards told the BBC.
"We got the first point, today we got our first win away from home in a difficult game for us, but let's not get carried away. In the end it's one win, three points," he added.
Led by energetic performances from Alfie Doughty and Chiedozie Ogbene, the Hatters defended cleverly in the second half, seeking to win throw-ins to relieve the pressure and trying to hold on to the ball, rather than just hoof it away.
"What I'm seeing is a team that's learning, it's evolving and adapting all the time. And I think we're growing and I like that I like the journey that we're on at the moment," Edwards said. "It's very early days, but we're progressing."
Luton move out of the bottom three to 17th on four points, behind Everton on goal difference, and Toffees manager Sean Dyche was again left frustrated by his team's performance.
"I'm disappointed because I've spoken endlessly about trying to change the story... we didn't score then we conceded two set-pieces which is really frustrating," he told the BBC.
"Credit to them, they did that better than us and we didn't defend the two chances they had."