Fallows joined Aston Martin in April as part of owner Lawrence Stroll's recruitment drive having spent 16 years as one of Adrian Newey's key lieutenants at Red Bull.
The revised design team which also includes former Mercedes aero chief Eric Blandin created a car that Fallows says features 95% new parts, a figure that rivals have acknowledged is high given that a lack of rule changes and the cost cap would typically encourage a high degree of carryover.
After showing encouraging form in testing, Fernando Alonso topped Friday's FP2 and Saturday's FP3 sessions in Bahrain, indicating that the green car is in the mix with the established big players.
"Firstly, we are pleased with the car," said Fallows. "We targeted making a big step on last year's car. So in terms of the performance relative to that, we're definitely happy that we have made a step forwards.
"And we set some fairly aggressive targets for ourselves. And we did sort of largely hit those.
"And we came out of testing believing that we did have a car that we could work with, but where we sit relative to other people, I know you'd love me to give you a prediction, but I'm afraid we just simply don't know."
Fallows stressed that when it first ran the car it showed a good correlation with what the wind tunnel had predicted.
"The key thing for us going into testing was to make sure that the car on track is doing roughly what we expected from the wind tunnel numbers and from our simulations," he said.
"I think it's always gratifying as a technical team to have a car on the circuit which is kind of what you were expecting.
"And for us that's really what testing showed us, which is good. The car, it's relatively predictable.
"It's kind of doing the things we want it to do so that was a very positive thing for us. I think in terms of relative performance, it's really difficult to say.
"I'm delighted there's a lot of excitement around the team, but really, things are done so differently by different teams in testing that it's really this weekend that we get some inclination of how good the car is.
"I don't think we're necessarily surprised that we hit the target. It's just that you always have this sort of niggling doubt that something is going to not quite work or that your correlation will let you down and the car that you produce on track doesn't quite do things as you'd expect."
