The Colombian blew his chances of winning last year when he spun his Williams just 10 laps from the chequered flag and a sluggish start cost him dearly this time.
After qualifying third, Montoya was perfectly placed to mount a serious challenge to the Ferraris of Michael Schumacher and Rubens Barrichello but he lost sight of them almost immediately.
Montoya surrendered third spot when Spaniard Fernando Alonso speared his Renault down the inside, then dropped back to seventh place when he tried to tried to recover and went wide on the first turn.
"I didn't take advantage at all," Montoya said. "After that, I spent my race trying to find the right moment to overtake the cars in front of me but that was no easy job."
Montoya, who finished third in last year's world championship, overtook his team mate Ralf Schumacher to move to sixth but dropped back to 11th when he pitted on the 11th lap and eventually finished fifth.
Ralf Schumacher, by contrast, made a flying start from eighth on the grid and finished fourth to give Williams nine points from the race but said he was worried by the team's failure to catch the Ferraris.
"We were on a good strategy and the team did an excellent job in the pits," Ralf Schumacher said.
"Worrying is the fact is that at this race, we are missing one second from Ferrari, which I didn't expect.
"I believe this is down mainly to the design of their car as well as to some tyre graining for us, which we have to overcome.
"The whole of our package needs to improve slightly and this is going to take maybe a couple of races, but I am confident we can make it."
Chief Williams engineer Sam Michael said it was clear the team had some catching up to do but it was not all doom and gloom.
"Our performance today was not really enough compared to Ferrari or Renault but it is far from a bad result either," Michael said.
"We have got both cars in the points and we come away from Australia with second place in the championship.
"Now we are looking forward to the hot tracks in Malaysia and Bahrain."
