Toto Wolff says Mercedes wishes it could change its Formula 1 Canadian Grand Prix hypersoft tyre allocation, accepting neither of its drivers had "enough track time" on the compound.
Mercedes selected the fewest sets of the hypersoft for the Montreal weekend of any team, and both Hamilton and team-mate Valtteri Bottas have three fewer sets available than all of the Red Bull and Ferrari drivers.
Neither driver tried the compound in Friday practice, and instead had to wait until Saturday morning's third practice session to use the hypersoft.
Wolff said he did not believe the allocation was the "decisive factor" in Bottas and Hamilton qualifying second and fourth respectively, but he conceded Mercedes' selection had compromised both drivers.
"This championship is going to be won or lost with the tiniest of margins, and certainly not having given the drivers enough track time on the hyper is something that if we could have changed it on the weekend we would have," said Wolff.
"We have just started driving on the hyper. Was that the decisive factor? Probably not.
"Would we have brought the engine upgrade it would have been an advantage.
"We just cannot miss out on the tiniest of upgrades or the smallest of mistakes or we will be penalised.
"The same applied for our competitors. This is going to make the difference between winning or losing the weekend."
Mercedes' decision came after pre-season testing indicated that the hypersoft had very high degradation.
Teams have to choose tyres 14 weeks in advance of flyaway races, meaning there was no opportunity for Mercedes to change its choices after the early-season races.
Hamilton said he would have liked to have spent longer on the softest compound in practice.
"I think we'll look back on this weekend and accept in hindsight it would have been nice if we had more time to prepare on the hypersoft but it wasn't the case," said Hamilton.
"The test we had in Abu Dhabi [in 2017] led us to the decisions we made - and we stuck with those."
Hamilton felt he could still have secured pole for Sunday's race but for problems at the hairpin in qualifying.
"In qualifying we knew it was going to be very close, but I truly feel we had the pace to lock out the front row, or at least I had the pace to be on the front row," he added.
"Yesterday [Friday], the car balance was great into Turn 10. Usually the last sector is actually my strongest at this track.
"But I was just struggling massively on the bumps into Turn 10 [on Saturday].
"As you continue to push the set-up, there are areas that can be affected.
"Constantly going into that corner I was struggling to get the car stopped, be it front locking, or rear locking. It was quite messy.
"There was a good chunk of time there. Definitely just in that corner alone was pole position, had I figured out how to fix it."