Introduction Triple negative breast cancer (TNBC) is highly heterogeneous, but still most of the patients are treated by the anthracycline/taxane-based neoadjuvant therapy (NACT). Tumor-infiltrating lymphocytes (TILs) are a strong predictive and prognostic biomarker in TNBC, however are not always available. Peripheral blood counts, which reflect the systemic inflammatory/immune status, are easier to obtain than TILs. We investigated whether baseline white cell or platelet counts, as well as, Neutrophil-to-Lymphocyte Ratio (NLR) or Platelet-to-Lymphocyte Ratio (PLR) could replace baseline TILs as predictive or prognostic biomarkers in a series of TNBC treated by standard NACT. Patients and Methods One hundred twenty patients uniformly treated by FEC/taxane NACT in a tertiary cancer care center were retrospectively analyzed. The presence of pathological complete response (pCR: ypT0/Tis, ypN0) or the presence of pCR and/small residual disease (ypT0/Tis/T1ab, ypN0) were considered as good responses in data analysis. Baseline/pre-NACT blood count, NLR, PLR and TILs were evaluated as predictors of response, distant recurrence rate and distant recurrence-free survival (DRFS). Results TILs ≥30% and ≥1.5% were best predictors of pCR and distant recurrence risk, respectively (p = 0.007, p = 0.012). However, in this cohort, pCR status was not significantly associated with recurrence. Only the ensemble of patients with pCR and small residual disease had lower recurrence risk and longer survival DRFS (p = 0.042, p = 0.024, respectively) than the rest of the cohort (larger residual disease). The only parameter which could predict the pCR/small residual disease status was PLR: patients with values lower than 133.25 had significantly higher chance of reaching that status after NACT (p = 0.045). However, no direct correlation could be established between baseline PLR and metastatic recurrence. No correlation either was found between TIL and individual blood counts, or between TILs and NLR or PLR. Conclusion In this cohort, TILs retained their pCR predictive value; however PLR was a better predictor of the ensemble of responses which had good outcome in terms of less distant recurrences or longer DRFS (pCR or small residual disease). Thus, baseline PLR is worth further, prospective investigation together with baseline TILs, as it might indicate a good TNBC response to NACT when TILs are unavailable.