"We needed that bit of luck for Roger's goal to start us off, but after that we went for the kill and ended up well on top.
"We were slow and didn't dictate the pace of the game, so I changed it at half-time.
"We were a bit sloppy in the first half, perhaps we felt we just needed to turn up and it was going to happen.
"Sometimes you get games like that where you've got to do the dirty part.
"We needed to move the ball quicker. We had a spell in the second half where we did that and we got in front."
As the season has moved into the 2nd half so to speak Jones is looking for a solid promotion push.
"There are 22 games left and that's a lot of points to be fighting for," he continued.
"You never give up when chances are there. You'd never forgive yourself if you did that and other teams faltered.
"We are chasing the people we have to chase down - Burnley first, then Reading, Birmingham and Wolves.
"You keep chasing. That's what we've spoken about, you need consistency at this level.
"It's about picking up the points when you're not playing well and grinding out results.
"And when you're on good form - as we've been - you've got to capitalise on it and make sure you win the games.
"The Christmas period is vital for everyone and we've just got to keep it going, keep believing and chasing the teams above us."
Meanwhile Owls boss Brian Laws was proud of the effort put in by his thrown together side. Wednesday didn't have enough players to name a full bench. Only 4 subs were available to Laws.
"We were well-organised in the first half but Cardiff had a large slice of fortune for their opening goal," he said.
"Then they had a penalty and the judgement call from the officials must be spot on but the referee's assistant wasn't up to it today and should maybe pay a visit to Specsavers.
"No one gave us a chance this afternoon as we never had enough players to even fill our bench because of illness and injuries.
"We lost our shape a little after they scored but I have told the players I am pleased with the performance under all the circumstances."