The left-arm swing bowler, who represents Gujarat in Ranji Trophy, has picked 62 wickets in 16 first-class matches.
Dhoni, however, said that winning and losing go hand in hand in a tournament like IPL.
CSK rode on an unbeaten 72 off 27 balls by Ambati Rayudu to post 218/4, but it was overshadowed by Pollard's blitzkrieg, as he smashed eight sixes and six fours in his unbeaten 34-ball 87.
The defending champions reached the target of 172 with nine balls to spare.
K L Rahul's solid unbeaten half-century and a disciplined bowling effort helped Punjab Kings tame Mumbai Indians by nine wickets and snap their three-match losing streak.
Shikhar Dhawan scored a 42-ball 45 and added 53 runs with Steve Smith (33) for the second wicket. Once they were back in the hut, Lalit Yadav (22) and Shimron Hetmyer (14) held their nerve to take DC home in 19.1 overs.
Chasing a target of 151, SRH were bowled out for 137 in the final over.
Chasing a target of 153, KKR were on course reaching 122/4 in the 15th over before losing their way and ending up on 142/7.
Leg-spinner Rahul Chahar picked up 4/27, while Jasprit Bumrah and Trent Boult were too good for the KKR batsmen at the death.
Royal Challengers Bangalore pipped defending champions Mumbai Indians by two wickets in the opening match of IPL 2021.