Smith saw his men shrug off both a sluggish start and a16-14 half-time deficit to eventually run out deserving winners, with Rhys Evans scoring four tries.
But the Wolves boss accepted things had to change at half time and said: "I was not happy with the way we played in the first half but I was never unduly worried.
"We came prepared for a tough game and that is what London gave us.
"Once we started playing with the intensity and speed in the second half we were going to be fine.
"It took us a little bit of time to come to terms with the narrow pitch, and the way London played, but in the second half I was pretty pleased."
Despite Roy Asotasi opening the scoring for the visitors inside four minutes, the Wolves were stunned when the Broncos ran in three tries of their own.
Nick Slyney, Ben Farrar and Thomas Minns all touched down to have the Londoners sniffing an upset. But Warrington struck back with crucial tries from Chris Bridge and Rhys Evans before the break, and after the interval it was a very different affair.
London looked visibly tired, and Warrington took advantage with six further scores. Gene Ormsby grabbed the first, Evans showed quickness of feet to claim three more, and Ryan Atkins helped himself to two, including a length of the field interception try on the hooter.
Broncos coach Tony Rea said: "I was really unhappy with how we played in the second half.
"I did not think we applied ourselves in the right way. Too many players were thinking about the scoreboard, rather than carrying on what they had been doing.
"We were looking to win the war, but Warrington made sure they won all of the battles, and that is how you win the war.
"They ran harder than us and they tackled harder than us and that made the difference."
- Sports & Recreation
- Rhys Evans