Twelve minutes after replacing Danny Simpson, Amartey picked up a yellow card for a body check on Marcus Rashford, before receiving a second booking four minutes later to reduce the Foxes to 10 men.
At the time, the situation looked worrying for the 2015-16 champions as they were 2-1 down and had only 17 more minutes to salvage a point.
“I think it was a good game for us against a great team," Puel said, as reported by his club's official website.
"We started well in this game. In the second half, we started well also, with quality and we had a fantastic opportunity to score.
"Just after this opportunity we conceded the free kick and we had a sending off of Daniel Amartey.
"It was a difficult situation but we saw the fantastic spirit and character of the players.
“They proved that they can make good things on the pitch because they believed until the end that they could take something from the game."
Leicester were the first to draw first blood at King Power Stadium through Jamie Vardy.
Juan Mata, however, leveled the score five minutes to half-time, before adding a second on 60 minutes.
But Harry Maguire spared the home side's blushes with a stoppage time equalizer.
"It’s a fantastic feeling to take the point," Puel added.
“We made good opportunities and had good quality in our play. Even with 10 against 11, we played with good quality.
"We had good balance at that time and we kept the possibility of playing well and attacking against Manchester United alive.”
Eighth on the league table, Leicester will face Watford on Boxing Day.