The Brit finished fifth at the Bahrain Grand Prix on Sunday and sits third in the drivers' standings in his debut season with the Silver Arrows.
Mercedes have taken pole for the previous two races but have struggled with excessive rear tyre usage, and Hamilton says that they need to sort out these problems in order to compete with the frontrunners.
"I feel like we're holding on by the skin of our teeth," Hamilton told BBC Sport.
"The guys at the factory need to keep pushing because we're not that far off and if we can just make that next step we can close the gap with them.
"I'm very proud of what the team have done getting the car turned around to where we are already. I feel very fortunate to be where we are points-wise and finishing-wise but of course we need to keep pushing."
Mercedes sit fourth in the team standings, 45 points behind leaders Red Bull.