Wolves boss Nuno charged on to the field to celebrate with his players after Diogo Jota completed a hat-trick deep into stoppage time.
The hosts led 2-0 and 3-2 before Leicester twice battled back to level during the second half, with Demarai Gray and Wes Morgan on target either side of a Conor Coady own goal.
Morgan's goal came in the 87th minute, partially explaining Nuno's explosion of emotion.
"I was sent off, rightly so. You cannot go on the pitch," he told Sky Sports.
"It's a game where everybody enjoyed the result. It was a fantastic game of football with two teams who really wanted to play and win the game.
"After we have an advantage we should manage it better. We were happy and lucky at the end to get the win. In football it is never finished.
"I wish I knew what happened at the start of the second half [when Leicester scored twice in four minutes] – we have to look at it.
"From 2-0 up we should manage the game better. Now we are speaking with happiness and relief but we could be blaming ourselves for not achieving what we should have."
The theme of poor game management was also present in Claude Puel's analysis, with the under-pressure Leicester boss stating his team should have settled for the draw Morgan appeared to have salvaged.
"We have had a lot of emotion in this game, different feelings of course," he said. "It was a poor performance at the beginning of the game.
"Without some saves from Kasper [Schmeichel] it could have been worse.
"After the second goal we came back with good intentions in the game, good pressing and good quality.
"We came back in the second half with fantastic desire. We managed come back - it was a fantastic feeling. We maintained our pressing and our physical activity but we conceded a third goal.
"We had the happiness to equalise and normally it is finished but we didn't keep our structure. We wanted to score another goal and it is our fault sometimes.
"To concede this goal is difficult. Sometimes we should keep our calm and composure for a draw. It is a big, big disappointment."