Hamilton had been poised to win at Albert Park but a timing error on the Mercedes pit wall during a virtual safety car period gifted the victory to his rival Vettel.
Even before news broke of his penalty, the 33-year-old already appeared to be playing catch-up.
Hamilton was only fifth and fourth respectively in yesterday's practice sessions with Ferrari's Kimi Raikkonen setting the pace ahead of team-mate Vettel. the Italian team seemed to have the advantage over Mercedes in the hotter temperatures.
Speaking before his grid penalty was revealed, Hamilton said: "We definitely have got some work to do to try and see if we can eke out to be ahead of the others.
"Practice has shown that it's incredibly close between the three teams. It will be a tough weekend."
Hamilton's teammate Valtteri Bottas will also take on a new gearbox, but, under the sport's rules, avoids a penalty as he is permitted a free change after his qualifying crash in Australia.
Raikkonen and Vettel finished half-a-second clear of their Mercedes rivals in practice. Kiwi driver Brendon Hartley clocked the slowest time in practice but believes signs are promising for the main race.
Hartley trailed the field in the second practice session in Sakhir, recording the slowest time of 1 minute 32.908 seconds, more than 3s slower than Raikkonen.
Despite putting in more laps (38) than anyone else in the 20-strong field at the 5.4km desert circuit, the Scuderia Toro Rosso driver couldn't eke anything extra out of a car which is on the verge of an upgrade.
Hartley was encouraged by the eighth-ranking from his French team-mate Pierre Gasly, whose car was fitted with new parts.
"It was a pretty productive day for the team," Hartley said. "Pierre and I ran very different set-ups across the cars as we had new bits to test.
"We definitely seem a lot more competitive than in Melbourne and it looks positive for tomorrow."
Hartley was 15th in Australia.
- Telegraph Group Ltd
