A blistering start from openers Dwayne Smith (66) and Brendon McCullum (67) helped CSK set a commanding total of 205-4, but the two-time champions were unable to defend it as Glenn Maxwell (95) and David Miller (54*) spearheaded a stunning chase that secured victory with seven balls to spare.
"When you score 200, you have to remember the opposition has every chance of scoring it as well," Dhoni told reporters. "It was a fantastic wicket, they batted really well. We did well but they beat us fair and square.
"We should have done better with the ball. Batsmen did their job and bowlers should have had different plans for different players. Bowl right areas. The margin of error is very small. There was not much spin."
Next up for Chennai is a game against the Delhi Daredevils on Monday.