Basicity of heterocyclic compounds
Furan and thiophene are going to be even less basic than their saturated counterparts, which can act as Lewis bases but aren't particularly well known for acting as Brønsted bases (very strong acids can significantly protonate ethers and sulfides, but not weak ones). They do, however, have a free $\mathrm{sp^2}$ lone pair with which they can bind a proton, but only one, unlike the saturated analogues, and an $\mathrm{sp^2}$ lone pair is going to be even less basic than a an $\mathrm{sp^3}$ lone pair because the electrons are closer to the nucleus (i.e. $\mathrm{sp^2}$ is "smaller" and closer to the nucleus than $\mathrm{sp^3}$).

Pyrrole, however, might be expected to be basic, but it also is not, as you rightly expected. This is due to delocalization of the nitrogen lone pair to create aromaticity. The $\mathrm pK_\mathrm a$ of the conjugate acid of pyrrole is $-3.8$, which is lower than that of even sulfuric acid, suggesting pyrrole is a very weak base.

All of those heterocycles are less basic than $\ce{Cl^-}$ or $\ce{H2O}$, so either your lecturer is incorrect or has been misunderstood.