Klopp ran onto the pitch and hugged Reds goalkeeper Alisson, after Divock Origi pounced on a howler from Jordan Pickford to snatch a victory for Liverpool.
The last-gasp goal ensured Liverpool beat their local rivals and kept the pressure on Premier League leaders Manchester City.
Klopp apologised for his exuberant celebrations immediately after the game, and could now be hit with some kind of punishment from the FA.
Some pundits and fans have labelled Klopps actions disrespectful, but Shaqiri played down the criticism of his manager.
The man is emotional and you can saw that in that moment, Shaqiri told Sky Sports.
When you score the last minute in a derby [in a] fantastic game, theres a lot of emotions in there. That happens in the game.
Many coaches [have] done that also. Its something nice and good, but of course its not to disrespect the opponent.
This is emotional and this is football. That happens. It was really nice to see these emotions from a coach.
Liverpool were lucky to snatch three points against Everton after a putting in a disappointing performance overall.
Everton were denied twice by Alisson, with the Liverpool stopper saving a close-range header from Andre Gomes in the first half.