After a double retirement in the first race, Verstappen and team-mate Alex Albon finished third and fourth in the second, but off the pace of Mercedes, which led to the Dutchman proclaiming the RB16 was "just too slow".
Assessing the gap between the teams' two cars, Monaghan said: "You can look as I can as to where we are slower than the Mercedes, and it's a little bit everywhere, so we've got a bit of work to do.
"It looks like their engine is pretty strong, it looks like the car is strong, and it's going to be a tough challenge to catch them, so let's see if we can. It's not insurmountable, it's not impossible."
For this weekend's Hungarian Grand Prix, the tight, twisty Hungaroring could favour Red Bull as it had the edge over Mercedes in the slow-speed corners in Austria.
"Hungary is a different sort of circuit," added Monaghan. "It's got a trivial straight and lots of twisty bits, the speed of the corners is lower than the Red Bull Ring, they're all the same speed.
"Typically, Hungary is less conflicted by variable weather than being in the Alps, and usually it's quite windy there, so a different sort of set of challenges. Who knows, we might be better there.
"We'll pick ourselves up, we'll update the car as best we can, and go there, try and give them a decent fight and hopefully beat them."
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