Kapil was the only ODI bowler to have got a hat-trick at the iconic Eden so far.
Kuldeep, who also thanked skipper Virat Kohli for supporting him, had earlier taken a hat-trick for India in the under-19 World Cup in 2014 opposite Scottland.
But he rated the one at the Eden Gardens as special as it helped fashion a 50-run win for India, who now lead 2-0 in the five game series.
"This is very special for me. That really changed the game for us. It was a proud moment."
Kuldeep conceded that in he was struggling with the leather in the first five overs.
"The first five overs I was struggling to bowl in a particular area, but later on I got the spot, and the rest is history."
It was also a story of contrast for Kuldeep who had been smacked for three consecutive sixes by Glenn Maxwell in the series opener at Chennai four days back.
"In game of cricket, everything happens. And in the last game, I got hit three sixes in an over," he said.