Three-time Tour de France champion Froome had started the day needing to make up one minute 12 seconds on Australia's Orica-Scott rider Howson.
He launched a couple of attacks over Sunday's fourth stage near Melbourne but was unable to narrow the deficit.
"Tactically we made some very different choices this year," Froome, 31, said.
"It didn't pay off for us, it went in Damien Howson's favour and hats off to him, he's ridden a really good race."
Froome's compatriot and Team Sky team-mate Stannard beat New Zealand's Aaron Gate as 10 riders vied for the stage win.
Howson cemented his first overall race win by finishing in the peloton alongside Froome 17 seconds later.
The final 121km (75 miles) stage featured four laps of Kinglake, with a 9km ascent on each circuit but the climbs were not difficult enough for Froome to engineer a break and he finished the day as he started it, in sixth place.
Meanwhile, Nario Quintana, twice a runner-up to Froome in the Tour de France, started his season with a victory at the Tour of Valencia in Spain.
The Colombian is targeting a Giro d'Italia-Tour de France double in 2017.
Stage four result:
1. Ian Stannard (GB/Team Sky) 2hrs 52mins 44secs
2. Aaron Gate (NZ/Aqua Blue Sport) Same time
3. Taco van der Hoorn (Ned/Roompot-Nederlandse Loterij)
General classification:
1. Damien Howson (Aus/Orica-Scott) 15hrs 25mins 13secs
2. Jai Hindley (Aus/Australian National Team) +38secs
3. Kenny Elissonde (Fra/Team Sky) +53secs
Selected:
6. Chris Froome (GB/Team Sky) +1min 12secs
Britain's Ian Stannard took the final stage of the Herald Sun Tour but Chris Froome was unable to defend his overall title as Damien Howson held on to win.