Hamilton only managed the seventh-fastest time of second practice, just over a second down on Verstappen, while Russell was well down the order in 15th.
Speaking after practice in Miami, Hamilton admitted it was a “struggle” for the team.
“The same as every weekend, that we’re a second down,” he said. “It’s a great weekend, it’s a great place to be. There’s lots of positives. It’s just we’re not particularly quick and it’s a struggle out there.
“We’re trying lots of different things. P1 looked quite good and then in P2, the true pace came out and it’s just a kick in the gut. It’s a little bit tough to take sometimes but it’s okay, we’ll just keep on working on it.
“We’ll regroup tonight and see if we can make some setup changes and get the car in a sweeter spot.”
Mercedes are pinning their hopes on a substantial upgrade package which is set to be introduced at Imola later this month.
Hamilton is hopeful that this is the start of a “new path” for the team in F1 2023.
“There isn’t just one thing,” he added. “I’m trying to stay positive with it. We’re working as hard as we can it’s just we desperately need those upgrades, that’s for sure.
“Just got to keep our head down for one more race and hopefully we’ll start a new path at the next race.”
Teammate Russell shared Hamilton’s frustration, stating that they will only be happy when they’re winning again.
“This is a team of winners, everyone here wants to win and anything less is of course frustrating,” Russell said. “Week after week we know the journey we’re on at the moment.
“Still trying to understand, still trying to grasp how to find a lot more performance to at least get us best of the rest. When we have sessions when we’re not in that position of course it’s frustrating - we always want more but that’s the same for 19 out of 20 drivers on the grid.
“There’s only one person happy on a Saturday, one person happy on a Sunday and that’s the one who finishes first.”