How does vorticity change the lift coefficient of an airfoil?
Shed vortices from unsteady flow over an airfoil result in decrease and phase lag in lift.

Ref: https://www.researchgate.net/figure/Vortex-shedding-from-an-airfoil-oscillating-in-pure-heave-2_fig2_251006855
Using thin airfoil theory in incompressible flow, the lift coefficient for an airfoil undergoing cyclical pitching and/or heaving can be expressed as (Ref. Drela, Flight Vehicle Aerodynamics):
$$C_l=\text{Re}\{ C(k)C_{l_Q} + C_{l_A} \} + C_{l_0}$$
$C_{l_Q}$ is the circulatory part of the lift, which, at steady-state, is equal to $2\pi\alpha$. $C_{l_A}$ is the non-circulatory part that have to do with fluid inertia; at steady-state, its contribution would be zero. The last term is the camber contribution. $C(k)$ is the Theodorsen function, which serves as a complex gain on the circulatory part of the lift. $\text{Re}$ here refers to the real-part of the function, not Reynolds number.
The decrease in lift and lag is readily seen in the Theodorsen function, where $C(k)=F(k)+iG(k)$:

Ref: https://pdfs.semanticscholar.org/8457/c72b980f2f129a9f211617a5cdee4e162b75.pdf
The reduced frequency, $k=\frac{\omega c}{2V_\infty}$, denotes how many airfoil chord lengths per flow distance traveled in one motion period ($\omega$ is the angular frequency of the cyclic motion), and is a measure of how much the cyclical motion affects the flow on the airfoil. As $k \to 0$, there is no attenuation in lift and no phase lag; this is the quasi-steady aerodynamics. As $k$ increases, there is increasing attenuation in lift, up to 50%. The maximum phase lag occurs at $k \approx 0.25$.
For most rigid-body motions in commercial aircraft, the reduced frequency is low and the quasi-steady assumption is valid.