"Malky's done a fantastic job, you have to give him a lot of credit," Pulis told the Western Mail.
"They were remarkably consistent in the Championship and deserved to win the title. Cardiff have every chance of establishing themselves in the Premier. Look at the teams who have been promoted in recent seasons. Many have done well.
"Look how Swansea pushed on and established themselves. Cardiff have got every chance. It's an enormous football club for me in an enormous catchment area. Malky has signed his first player as a Premier League manager and I'm sure there will be more. They need enough to get a foothold and progress.
"I like Malky, the way he goes about his business. Quietly, efficiently. He has done a remarkable job for Cardiff. Malky gets things done, quietly and efficiently.
"I hope all the people at Cardiff City are looking at the new season in a realistic way. They need to be patient, it's important everybody sticks together."