It is rather hard to identify the grass from the image, which doesn't show many of the major distinguishing characteristics of crabgrass. It does look like an annual grass that does not have rhizomes, which fits. The leaf blades of crabgrass are much wider than typical lawn grasses, usually lighter green in color and the plant is usually found along the edge of gardens and flower beds and also growing in lawns, particularly if the lawn is not very vigorous, soil is compacted or if it is being mowed too short. The seed head is finely textured but spreads out from a single point, kind of like a turkey foot, See the attached pictures for some views of how crabgrass usually looks.