Jacob Brown headed home Alfie Doughty’s 57th-minute corner to earn the Hatters a first win in four games.
And it moved them above the Bluebirds, who came into the game on a six-match unbeaten run.
“I think we played well, but you can see Cardiff are playing well at the minute,” Edwards said.
“They’ve got a good rhythm, a confidence and belief there, the run that they’ve been on and some very good players as well.
“After the first 15 minutes or so where we didn’t quite arrive quick enough in some of the pressing, after that we got to grips with it.
“We won it back a lot and I think the game was where we wanted it to be. They might have had the ball a little bit but we’ve got to try and keep it as far away from our goal as possible, which we did.
“I think that we certainly had the majority of the momentum and the game was where we wanted it to take place, so I think we deserved the win, but it was a night where it was important.”
Cardiff did not seriously threaten a leveller and their first defeat in seven left them sitting above the drop zone on goal difference.
Interim boss Omer Riza said: “I think the boys are really disappointed.
“To be undone with a set-play, which we know they’re strong at, was disappointing.
“Overall the performance wasn’t too bad. I thought we controlled some big parts of the game, it just wasn’t quite there today.
“We didn’t quite click the way we have done recently with our attacking threats. We still picked up good pockets, we still received the ball, we still pulled the opposition into positions they didn’t like, but just those final moments, we weren’t calculating enough.
“If we had been, I think we probably would have created a bit more, but credit to Luton, they got their result and we move forwards.”
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