Referee Graham Scott reached into his pocket but showed Kompany just a yellow, which the home fans inside the King Power Stadium were left angered by.
The Citizens took the lead late in the first half through Gabriel Jesus and netted another early in the second in what turned out to be a straightforward victory for the league leaders.
Speaking to Sky Sports News at full time, Puel questioned the referee's decision to let Kompany remain on the pitch and claimed that it may have been a different game had a red been awarded.
"The result is hard of course, it is not good to lose a game but I think there were different events in this game," he said. "Yes, of course [the game was defined by small margins] because there are so many events in this game.
"The first move for us and the foul from Vincent Kompany, I think it's a red. This action can change the feel of the game. I think for the first 30 minutes, we played good football with good organisation and we had some good moves but it was a bit more difficult at the end of the first half.
"It was a pity that they scored just before half-time and to take the second goal quickly just after the kick off in the second half, I think it is pity because we hit the post. We have to score in this moment and then they counter-attacked for the second goal. We need to keep going with this in the future because it was promising and after, we know we need to make progress with the ball just after our recoveries and our organisation.
"The feeling with the players is very good, they listen and this is very important for the future. I think for the second part of the season, against Manchester City, we will see another game and another team."
Leicester have now lost their last nine Premier League games against sides who started the day occupying top spot in the division, conceding at least two goals each time.