They were definitely more balanced teams than some of the recent vintages. The 2001 offense wasn't very good, so its not surprising they weren't very good in the playoffs. The '03 offense was decent but worse than every offense that came afterwards (including the Cassel season), and those first two playoff games were both played in shitty conditions. '04 offense was excellent/elite and played generally very good in the playoffs. Slow start in the Indy game, but another game in not great conditions and a great 4th quarter clock killing drive. They were good but not great in the Super Bowl.
Offense has played a lot of good games in the playoffs as well though. (Carolina SB, Pitt '04, Jacksonville '05, NYJ '06, Indy '06, Jacksonville '07, Denver '11, Hou '12, Indy '13). Even in the losses mostly it was just the offense not playing at its usual high standards and not a total stink bomb where they couldnt do anything with the exception of the '09 Ravens game, the first Giants Super Bowl and (to a lesser extent) Denver '05 (turnovers) the 2nd Giants Super Bowl (few possessions skewed the score low and they moved the ball generally OK, just didn't capitalize), Ravens '12 (moved the ball well for 35 minutes, but too many missed chances then the turnover fest started) and last years AFC title game (valiant effort with a skeleton crew and they at least found something in the fourth quarter)