McLaren say claiming a podium finish at this weekend's British Grand Prix will be "challenging" for their drivers.
The Woking-based team have endured a difficult season, with neither Briton Jenson Button nor Mexican Sergio Perez finishing higher than fifth.
McLaren managing director Jonathan Neale says taking points in Sunday's race at Silverstone is a realistic aim.
"We are pushing hard but the reality is there is still a big gap from us to the front of the grid," he said.
"Based on recent past performances I think (a podium) could be challenging. I want to get both cars into Q3 and then race hard for good points.
"Formula 1 is a fickle sport and you never know what can happen, but we're realistic about our prospects of a win."
He added: "There isn't going to be a golden bullet."
Both Button, 33, and 23-year-old Perez failed to pick up any points at the Canadian Grand Prix, finishing 11th and 12th respectively.
Consequently, McLaren are sixth in the constructors' championship with 37 points, 164 behind leaders Red Bull.
McLaren used one of their allotted straight-line test days in Spain on Tuesday to trial their Silverstone upgrade package, as well as gain a better understanding of the MP4-28.
"The only issue with our car is we lack downforce and that is what we are trying to create at the moment," Neale said.
"We've got a range of upgrades for the weekend but we're not there just testing parts, but testing some fundamental understanding issues as well."