Rovers scored three tries in the opening 20 minutes as they established a 16-0 lead at half-time and there was no way back for Saints after that as they suffered their first home loss against the Robins since 2009.
Brown, who took charge of Saints after leaving Huddersfield after last season, said: "I can't fault our effort but we never got in the contest and it was our most disappointing performance since I've been here."
Hull KR, who had Travis Burns and Mickey Paea sin-binned by referee Robert Hicks, scored three tries to two with Michael Dobson booting six goals from seven attempts. The Rovers tries in the first half came from Burns, Alex Brown and Greg Eden with Saints replying with second-half touchdowns from Francis Meli and Anthony Laffranchi.
Home skipper Paul Wellens was yellow-carded alongside Burns after a first-half flare-up with Saints failing to capitalise on a 16-8 penalty advantage.
Brown, whose side had claimed impressive victories over Bradford and Salford in their previous two matches, added: "Our attack was poor. They kept kicking the ball behind our wingers and we did it once. They kept forcing us into errors and we weren't smart.
"It was disappointing for the fans because we are capable of better than that. We had been building along nicely recently but we have taken a step backwards. I didn't think their first try was a try but we didn't respond to that."
In contrast to Brown, Rovers coach Craig Sandercock was understandably delighted with his team's gutsy display after seeing them make it five wins in their last six games. It was also their third victory of the season over St Helens and saw them climb above cross-city rivals Hull into sixth place in the Super League standings.
Sandercock said: "It was a big win and gives the boys a belief they can win away from Craven Park. We were outstanding defensively.
"We conceded too many penalties for my liking but we showed great defensive resolve. Usually our attack is not too bad but it's our defence that gave me the most pleasure."
- Sports & Recreation
- Travis Burns
- Mickey Paea