Rovers scored four tries versus dynamic opponents and caused plenty of problems, leading 20-18 in the second period.
Saints – who have lost just one of their 14 games so far – ultimately got home but Sheens said: “They average about 33 points a game against everybody in the comp’.
“They are without doubt the competition favourites at this stage of the season.
“We scored 24 points against them earlier this year and 26 good – not fluky – points today which is the most anyone has since the middle of last year.
“And it was against a very strong side; today was pretty much close to their strongest side. I thought we performed really well. We certainly gave them a game, there’s no doubt.”
Sheens added: “There were good moments – and a couple of terrible moments for us.
“But the guys didn’t give up. People don’t understand when I say you can get beat or you can lose; we lost a game today but we didn’t get beat.
“People kept turning up and kept trying which is the biggest thing. The majority of the crowd stayed to show their appreciation and that’s all you’re looking for every week from the side.”
Rovers remain in 11th, though, after a fourth straight defeat.
Saints’ classy right-edge of Fiji centre Kevin Naiqama and England winger Tommy Makinson both scored hat-tricks.
Sheens added: “Our left-edge helped them a bit too. That was where most of the points came and once they sorted us out down there we were in a bit of trouble.
“We had to make some changes before the game which moved Jimmy Keinhorst out of there (centre) and Junior (Vaivai) back in to his favoured spot.
“I’ll wear the blame on that. We didn’t gel on that side as we changed things before the game.
“We had to with a couple pulling out. I needed a back-row and Jimmy put his hand up to play there for Joel (Tomkins).”
Saints coach Justin Holbrook said: “Credit to KR – right from the start you could tell they were going to give it their best shot.
“But we did well to turn it around in the end.”