Having been written off when joining the Silver Arrows at the start of the year, the 28-year-old believes that he is surpassing what was expected of him this campaign.
"I'm very proud of what we have achieved over the first four races and to be third in the championship is beyond any of our expectations," Hamilton told BBC Sport. "But we've got to keep pushing and find more performance.
"We're hanging on by the skin of our teeth at the moment and, if we can make that next step, then we can close the gap."
Hamilton had finished third in his previous two races.