Alonso and team-mate Lance Stroll struggled to maintain their excellent early-season performance in qualifying at Baku's high-speed street circuit.
Speed traces from Q3 indicated that neither driver gained top speed in Baku's two DRS zones, and afterwards the pair confirmed that Aston Martin's DRS was malfunctioning.
"I think we could have been a little bit better," said Alonso, who qualified sixth a full second behind Ferrari's polesitter Charles Leclerc.
"We had some issues in FP1 and also in qualifying with the DRS, which cost us a few tenths. Being so tight, I think in the standings it will make a difference.
"But, nevertheless, it's only Friday. It's a long weekend ahead of us. Another qualifying tomorrow, another race and then the race on Sunday. So yeah, plenty of opportunities so hopefully we can pick up a few places."
Stroll confirmed that he too didn't have a working DRS system as he settled for ninth, 1.4s adrift from pole.
"The car felt good, but we had some DRS issues," the Canadian added. "In Q3 especially I didn't have DRS, so that costs some time.
"It's just free lap time down the straights so that was frustrating, but we've just got to try and sort that out for the race."
Team principal Mike Krack thought the DRS issues masked Aston Martin's true potential and was therefore confident both drivers could move up the grid once the gremlin is resolved.
"Both Fernando and Lance did well under challenging circumstances today," said Krack.
"The single practice session was quite straightforward but, going into qualifying, we experienced an ongoing DRS issue across both cars, which meant it was only working intermittently.
"Despite this costing us some performance, we progressed to Q3 quite comfortably and the team and drivers did a good job of managing a busy session with the yellow and red flags.
"We had the potential to be a bit higher up the grid, but I think we are well placed to fight for points on Sunday and this is a circuit where overtaking is possible."