Speaking ahead of this weekend's Azerbaijan Grand Prix, the seven-time champion stressed that a win was unlikely, but that a top-three finish was realistic in the final eight races.
Hamilton has never gone through a complete season without a podium finish and has faced mounting criticism of his declining form, including a warning from former F1 ringmaster Bernie Ecclestone to retire before he is forgotten.
"I feel optimistic coming into the weekend," said Hamilton.
"I feel like I've found a couple of things and now I need to work on extracting them. So, I really hope that this weekend can be the start of that."
He said a win would be "far-fetched considering I've been sixth, seventh and eighth for most of the season, but I'd love to get a podium for the team at some stage. Charles (Leclerc) has five of them."
Like Hamilton, Leclerc has also endured a disappointing season with Ferrari, but he heads into this weekend's contest seeking a fifth consecutive Baku pole.
He said after the Italian race that he felt Baku, Singapore and Las Vegas would all offer Ferrari a chance to move closer to McLaren at the front of the field.
Champions McLaren are set to retain their constructors crown this Sunday if they finish nine points clear of Ferrari.
"I still have this feeling, mostly based on many years coming here, and most of the time we were not the favourites on paper, then we ended up having pole," said Leclerc.
"But that doesn't mean we can win on Sunday. Pole position puts you in the best possible place to start, but that doesn't necessarily mean that we will have the race pace.
"That's what we've been lacking in past years and I don't have a big hope that this year is going to be significantly different."