Drought stress is a global problem, and the lack of water is a key factor that leads to agricultural shortages. MicroRNAs play a crucial role in the plant drought stress response; however, the microRNAs and their targets involved in drought response have not been well elucidated. In the present study, we used Illumina platform (https://www.illumina.com/) and combined data from miRNA, RNA, and degradome sequencing to explore the drought- and organ-specific miRNAs in orchardgrass (Dactylis glomerata L.) leaf and root. We aimed to find potential miRNA–mRNA regulation patterns responding to drought conditions. In total, 519 (486 conserved and 33 novel) miRNAs were identified, of which, 41 miRNAs had significant differential expression among the comparisons (p < 0.05). We also identified 55,366 unigenes by RNA-Seq, where 12,535 unigenes were differently expressed. Finally, our degradome analysis revealed that 5950 transcripts were targeted by 487 miRNAs. A correlation analysis identified that miRNA ata-miR164c-3p and its target heat shock protein family A (HSP70) member 5 gene comp59407_c0 (BIPE3) may be essential in organ-specific plant drought stress response and/or adaptation in orchardgrass. Additionally, Gene ontology (GO) and Kyoto encyclopedia of genes and genomes (KEGG) analyses found that “antigen processing and presentation” was the most enriched downregulated pathway in adaptation to drought conditions. Taken together, we explored the genes and miRNAs that may be involved in drought adaptation of orchardgrass and identified how they may be regulated. These results serve as a valuable genetic resource for future studies focusing on how plants adapted to drought conditions.