It is now well established that water-like anomalies can be reproduced by a spherically symmetric potential with two length scales, popularly known as core-softened potential. In the present study we aim to investigate the effect of attractive interactions among the particles in a model fluid interacting with core-softened potential on the existence and location of various water-like anomalies in the temperature-pressure plane. We employ extensive molecular dynamic simulations to study anomalous nature of various order parameters and properties under isothermal compression. Order map analyses have also been done for all the potentials. We observe that all the systems with varying depth of attractive wells show structural, dynamic, and thermodynamic anomalies. As many of the previous studies involving model water and a class of core softened potentials have concluded that the structural anomaly region encloses the diffusion anomaly region, which in turn, encloses the density anomaly region, the same pattern has also been observed in the present study for the systems with less depth of attractive well. For the systems with deeper attractive well, we observe that the diffusion anomaly region shifts toward higher densities and is not always enclosed by the structural anomaly region. Also, density anomaly region is not completely enclosed by diffusion anomaly region in this case.