Punjab were strangled by some quality spin bowling by Sunil Narine and Piyush Chawla as they could manage 131 for nine in their 20 overs.
However, Kings XI bowlers produced a disciplined effort to compensate for their dismal batting display and bowled out Kolkata for 109 with 10 balls to spare and Bailey described it as "outstanding".
"Bowlers were outstanding. Probably left 20 or 30 short on a tough wickets but we knew we had a chance if we took early wickets," Bailey said after the match.
Bailey also heaped praise on pacer Sandeep Sharma, who returned with three crucial wickets.
More From This Section
"It's good to see Sandeep develop, he's got great confidence in what he wants to do which makes my job easier," he said.
Kolkata skipper Gautam Gambhir also praised his bowlers for restricting Punjab to a modest total but said it was their batting which needed attention.
"The bowlers did a fantastic job, we should have chased it down. We have to sort out batting," said Gambhir.
Talking about Albie Morkel, he said: "Morne is an aggressive bowler and so far he's been brilliant. He is a wicket-taking bowler."
He also had a word of praise for young Suryakumar Yadav, who tried to lead a fightback at the end with a 17-ball 34.
"Surya looks a very talented cricketer and he'll get many more opportunities and at a better number," Gambhir said.
Sandeep Sharma, who was adjudged as the Man of the Match, said: "It's a big moment for me, enjoying a lot, Expressing myself. When I'm playing I'm very serious, outside the rope I'm very funny.