Massa had outqualified Alonso and was running ahead of his team-mate through the first two stints.
But before the second pitstops, Alonso came in early and was able to leapfrog both Massa and leader Sebastian Vettel thanks to a clear lap on fresh tyres.
Massa denied this was a case of Ferrari putting Alonso on a preferential strategy and said he would not have wanted to pit when his team-mate did because in theory the tactic should not have worked.
The Brazilian felt Ferrari needed to get at least 15 laps out of each set of tyres, whereas Alonso pitted after 11.
"When you're fighting with the guy at the front and then you lose two positions, you're always disappointed," Massa said.
"Honestly it was a little bit too early to stop. We were planning to stop maybe three or four laps after.
"Looking at the degradation on the tyres, it was quite high. But he took a risk and it worked."
Massa felt track conditions moved in Alonso's favour.
"The track improved and it was much better for keeping the pace with more rubber on the track, and he didn't have any cars in front," said the Brazilian, who ultimately finished fourth.
"So it worked. For sure when you are behind it's always easier to stop before and try to take the risk.
"I am a little bit disappointed about this but overall I'm happy because the way we started the season was very, very positive."
AUTOSPORT Australian GP coverage:
FP1 FP2 FP3 Qualifying Race Gallery Live commentary Official quotes
- Sports & Recreation
- Motor Racing