Saints recorded a comprehensive 31-10 victory over the Black and Whites.
“I thought Swifty had a great game. He was going into it with a little bit of doubt and I thought he had a real good game,” Cunningham told Sky Sports.
“There was probably two or three big turning points in the game in that second half and Swifty was involved in all three of them.
“Defensively we were great. When you look at the tries they scored, it is a soft one in the corner and a one-on-one miss there.
“Everything else Hull threw at us I thought we defended exceptionally well but we have got to bring this home and bring it home hard.
“If you want to run with the wolves you have got to start playing like the wolves.
“Pardon the pun but we have got to play like the top four sides and we are in patches but we have got to consistently do it for 80 minutes.”
Although the Saints secured the win, Cunningham admits he was disappointed with the team’s start, going behind early on.
“I thought we probably took things a little bit for granted and we saw that there were a few names not on the Hull sheet and we probably fell in love with Hull’s Challenge Cup success last week as well,” he said.
“We did ourselves a little bit of an injustice in that first 20 minutes. Time and time again we are a little bit guilty. It’s the same as the Wigan game.
“We are giving away cheap possession and not getting a foothold in the game sooner.
“That final 20 minutes and the second half performance was much better.”