The Silverstone and Enstone teams have often been close rivals in recent years, with the transfer of team principal Otmar Szafnauer between the two camps and Fernando Alonso's move in the opposite direction adding an extra edge.
But in the two races held so far this year, Aston Martin has moved far ahead, with Alonso securing two third place finishes, while Alpine has not finished higher than eighth.
While Permane admits that the A523's current form is not good enough, he says the team is closer to Ferrari and Mercedes than it was last year.
"It's not satisfying that we're not where we want to be in terms of pace," he said. "We want to be a bit quicker than that, up fighting those guys.
"I think we are closer to Ferrari and closer to Merc than were last year. I haven't really had a good analysis of it yet, but I'm sure we're closer to Ferrari, because at this time last year, they were fighting for wins.
"Obviously, Aston have made a huge leap, and we're fifth quickest team, which is not where we want to be. Our target was to be closer to third place. That isn't the case at the moment. Actually, it may be, because if you say Mercedes is the third quickest team, maybe we're closer to them than we were last year.
"But it's not good enough. It's not where we want to be, and I think Aston have caught everyone by surprise by the jump they've made."
Permane conceded that it's going to be hard for rivals to catch Red Bull over the course of this season, but he remains confident that Alpine can improve its own car.
"It does look like no one's getting close to Red Bull this year, they look like they've got a second a lap in hand honestly," he said. "It's frustrating. We just need to keep working hard and bringing the upgrades and putting the downforce on. Keeping on keeping on, and that worked very well for us last year.
"We brought a lot of stuff last year, we've got good correlation. So we can be very confident that parts and upgrades we bring will work the car, we just need to improve it at a faster rate than the others do."
Asked where A523 car is lacking he said: "I suspect it's a little bit everywhere. The drivers want a little bit of an improvement in braking, they want some better traction.
"There's not one real area where they're really complaining about. We need to improve everywhere, I'm sure."
