Centre-back Harry Maguire scored a late equaliser for the 'Foxes' after Daniel Amartey saw red for two bookable offences after coming off the bench and United spurned a number of opportunities to make the game safe.
All things considered, Puel was delighted with his side's fighting spirit, saying: "It's a good feeling, it's a good game against a good team.
"The sending off was a little harsh but we saw fantastic spirit from the players. They deserved it.
"With a positive attitude we stayed in the game and continued to believe in ourselves. It's fantastic.
"It's a good result for all of us because the belief keeps going. It's fantastic for the future.
"Now we know if that situation happens again we can score with 10 men against 11, so that's a good feeling for the future."
The point saw Leicester retain eighth position in the Premier League, whilst United fell further off the pace, seeing the gap between them and runaway leaders Manchester City extend to 13 points.