Lucknow qualified for the playoffs with 18 points, while Kolkata finished the tournament with 12 points from 14 league games.
In the 17th over, fast bowler Mohsin Khan (3-20) ended Kolkata's hopes when Andre Russell was caught in the deep with the score at 150-6.
Despite the loss, Kolkata captain Shreyas Iyer felt his team demonstrated a lot of character and attitude in their final IPL game of the season.
“I’m not feeling sad at all because that was one of the best games of cricket I’ve ever played to be honest,” Shreyas said. “I love the way Rinku got us to the end … he was really sad. I was hoping that he could finish the game for us. He could have been the hero. Still, he played a fantastic knock and I’m really happy for him.”