George Russell finished FP2 in seventh place, 1.3s down on leader Charles Leclerc, with teammate Lewis Hamilton a further three tenths in arrears in 12th.
Both drivers appeared to suffer from severe bouncing issues again due to the floor bottoming out on the straights, which has also plagued the team in Monaco.
Shovlin admitted that a solution to Mercedes' Baku struggles goes well beyond fine-tuning, saying the team needs to look for "fundamental improvements".
"We've got a bit of work to do to find time on single lap and long run. The balance isn't a major issue but we're lacking grip in the corners and the ride on the straights is uncomfortable for the drivers, so we need to improve that overnight," he said.
"Our straight-line speed also isn't great but some of that will be due to us hitting the ground on the straights. We did have some new parts on the car today, so we'll review whether those were contributing to our issues.
"Overall, we're not in a good position and it's one where we need to be looking for some fundamental improvements rather than a case of fine-tuning."
Hamilton said the dramatic bouncing, which also affected other teams including chart topping Ferrari, was the "hardest thing" about his Friday.
"The hardest thing about today was the bouncing, I'm a bit sore," Hamilton explained. "We're hitting serious speeds at the end of the straight and bottoming out. We're facing the same problems as in the last race.
"We tried something experimental on my car in the second session, it didn't feel great but at least we tried it and we got some useful data to go through. We'll probably revert to the original set up tomorrow.
"I can't tell you one specific area which is costing us the 1.3 or 1.6 seconds difference to the front, a lot of it seems to be on the straight but we need to get our heads down tonight and find solutions."
Russell: Conversations with F1 needed on bouncing issues
Russell thinks the scale of F1's bouncing issues across various teams, eight races into the 2022 era, suggests that the sport should look at a long-term solution.
"Now with the cars running so close to the ground, in the high speed corners the cars are fully bottoming out and it's the same for everybody, it's really not comfortable to drive," Russell added.
"I don't know what the future holds for this era of cars, but I can't see us running like this for the next four years, so for all of us conversations will be needed as we're all in the same boat."
