Hamilton started the race in seventh place and finished it in fifth after passing team-mate George Russell and benefitting from the retirement of Ferrari's Charles Leclerc.
However, he was powerless to hold off the Aston Martin of Fernando Alonso, who had a bad start and eventually recovered to finish third.
Asked if he was concerned that the team hasn’t made much progress since last season, Hamilton insisted that his role is to keep the team motivated.
“Concerned wouldn’t be the word,” he said.
“There is nothing I can say, I don’t want to say too much. We’ve just got to keep working.
“We know we are not where we need to be, and we know that this isn’t the right car. It is a difficult one.
“But I’ve just got to try and stay positive, keep my head up and keep pushing the guys.
“Keep trying to be a positive light for them and get the best points I can.”
Hamilton dismissed the suggestion that he was closer to the podium than he expected to be after qualifying.
“We were miles away,” he said.
“There was a Ferrari that would’ve been ahead of him [third-placed Alonso], so we would’ve really been sixth. So a podium was nowhere near.”
Mercedes had strong race pace for much of the 2022 season, although the Bahrain opener saw the team struggle with tyre degradation. That pattern was repeated in Sunday’s event.
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“It generally felt the same as last year,” said Hamilton. “When we did the strategy in the morning I told the guys it wasn’t going to go as far as they said it was going to go, and it didn’t.
“We have just got a lot of work to do. We have just got to add downforce to the car, we’re lacking a lot of downforce.
“That is really where the time will come. As soon as we put more load on the rear and the front we’ll pick up that pace.”
Regarding the battle with Alonso, he said: “It was fun for a moment. He was in a different league at the time, performance-wise, as you saw, because he pulled away so much.
“But I enjoyed the little tussle that we had, and I knew he was going to come by, because of the way he caught me.”
He added: “Big congrats to Fernando today. He did a great job and it is really amazing to see, and to all the Aston Martin team, they did such a good job.
“We’ve got work to do, because half of their car is ours, and they built their car in our wind tunnel, they do their aero in our wind tunnel, so we’ve got some work to do.”
