Although associations between running performance (RP) with ball possession and team achievement in soccer are often hypothesized, actual knowledge of this association in elite soccer remains limited. Therefore, this study aimed to evaluate players’ RPs according to ball possession to determine its possible influence on team achievement in the UEFA Champions League (UCL). The players’ RPs (n = 244) were collected during UCL group stage matches (n = 20) in the 2020/21 season using the semiautomatic video system InStat Fitness. Then, players’ RPs were classified according to the specific playing position: central defenders (CD; n = 79), fullbacks (FB; n = 65), central midfielders (CM; n = 55), wide midfielders (WM; n = 28) and forwards (FW; n = 17). RPs were observed in the attacking phase (AP, i.e., when the team was in possession of the ball) and defensive phase (DP, i.e., when the team did not have possession of the ball) of the game, and included the total distance covered (m) and distance covered in different categories: walking (<7.1 km/h), jogging (7.1–14.3 km/h), running (14.4–19.7 km/h), high-intensity running (>19.8 km/h), high-speed running (19.8–25.1 km/h) and sprinting (>25.2 km/h). Team achievement was defined by the total group points earned (TGP) at the end of the group phase of the UCL and by match outcome (win, draw, loss) of single matches. The results indicated that the total, walking and jogging distances covered were negatively and positively associated with TGP (Pearson’s correlations from 0.30 to 0.73; all p < 0.05) in the AP and DP of the game, respectively. Won matches were characterized by significantly lower and higher values of total, walking and jogging distances covered in AP and DP of the game, respectively (F tests: from 7.15 to 22.5, all p < 0.01; all small to medium effect sizes). In addition, RPs in the AP and DP of the game explained only 37.2% of the variance in the TGP. These findings demonstrate that the influence of RP on team achievement in UCL is limited in both the AP and DP of the game.