The Saints climbed to the top of the Super League table with the win, which ensures that the Broncos remain winless with just five games of the season remaining.
"I thought for about 30 minutes we were on form and when we scored just after half time I thought it would be a blow-out," Brown is quoted as saying by Sky Sports News.
"But credit to London - I thought their effort was outstanding and they hung in there. In fact, considering the position they are in, I thought their attitude was excellent.
"I'm still pretty happy with the result overall. I wanted an improvement from last week and I think I got that, and some of our tries showed what we can do as a side."
Next up for St Helens is a home encounter with Widnes Vikings next weekend.