Brighton got a chance to lead at break when they got a chance from a spot kick, but saved by the goal keeper.
Kasper Schmeichel saved Neal Maupay’s spot-kick in the first period before City had a penalty shout of their own turned down in injury time after the ball struck Lewis Dunk’s arm in the box.
Speaking to LCFC TV at full-time, Rodgers said: “We didn’t create enough in the first half. [It was] two teams playing similar shapes, so there wasn’t many chances in the first half.
“Obviously, Kasper had the penalty save, which he’s absolutely brilliant at. Apart from that, we didn’t have to defend so much, especially second half.
“So, I was disappointed with the quality of the play in the first half, we didn’t have enough movement ahead of the ball. The second half, we were much better. I think our fitness came into it as well.
“The team showed a good level of fitness and were able to sustain the attacks and it just felt like it was goal was coming, but it wasn’t to be. But the players, I commend them, because it’s so difficult.
“We clearly haven’t found the rhythm of our game yet, but we’re trying and fighting at every opportunity to get the results that we want. We couldn’t quite make the breakthrough this evening.”
The Northern Irishman hopes City will begin to find their rhythm in the coming weeks, when they complete more training sessions and get more games under their belts.
Rodgers added: “I thought we kept pushing against a team that’s really dangerous. You see the result that Brighton had at the weekend. That tells you the quality that they have.
“So, for us, we knew this was going to be a really, really tough game, but I think the players in the short turnaround showed a really high level.
“We obviously tried to freshen it up, by changing it around a little bit, putting in an extra striker to try and get support to Jamie [Vardy].
“But we just couldn’t quite make the breakthrough. I was pleased with the second half, it was more like where we were at, now it’s just about making the final pass.
“So, with more training and hopefully with games, we hope to find that quickly.”