"We were a bit flat to start - it was 14-0 after four minutes."
Wanganui were 21-5 down at halftime as they turned to face the wind, but rallied to only trail 21-15 with 15 minutes left to play.
However, Wairarapa-Bush coolly regained momentum with a penalty, then scored the matchwinning try.
Wanganui's tryscorers were second-five Simeli Konifredi, who was their most influential player, and prop Gabriel Hakaria, along with one conversion and a penalty kick.
Williams didn't think the century scoreline his side put on Horowhenua-Kapiti Development last weekend had lulled them into a false sense of security.
"[Wairarapa-Bush] wanted it more, had a few Heartland boys drop down, which helped them.
"We were chasing our tail a bit. We didn't cope well with the travel."
The team will now have a bye before they face the Wellington Centurions back at Cooks Gardens, although given the RDO Shield is a round robin competition, they will need to win their remaining games while hoping Wairarapa-Bush stumble along the way.