As a Mariners fan, I can tell you that we've never even gotten to the point where we could actually point fingers at a single player and blame them for our lack of success. There was some finger pointing at Aaron Sele in the 2001 playoffs as having cracked under pressure, but that's as close as it's ever gotten.
For us, it's just the slew of terrible, counterproductive, horrible GMs we've had, such as Woody Woodward (1988-1999), Pat Gillick (2000-2003), and Bill Bavasi (2004-2009). Gillick and Bavasi were so terrible that they actually make Woodward look good, because he brought in Lou Pinella and acquired some talented players. He became infamous, though, for some spectacularly awful trades, such as the Slocum deal, which epitimizes terrible trades to this day.