If you think post-season games are taking a long time to play, you are correct:

This year’s overall postseason average of 3:38 is an increase from 3:32 last year.

Chron.com

There is a discussion of the pitch clock, which appears to make minor league games go much faster. The article also points out that there is much more commercial time between innings, which alone adds about fifteen minutes to the game.

It seems to me, however, that the post-season batters really work counts. Game five saw 317 pitches thrown to 82 batters. That 3.9 pitches per batter. Good hitters wait for their pitch, and are willing to take strikes to get that pitch. This is where a pitch clock could really help. If a clock saved five seconds a pitch, that means about 20 seconds per batter. For 82 batters, that 27 minutes saved.

A test was held this season at minor league Low-A West, setting the clock at 15 seconds with the bases empty, 17 seconds with runners on, 30 seconds between batters and 2:15 for half-inning breaks and pitching changes.

The 316 nine-inning games with the clock averaged 2:41, down from 3:02 for the 91 games without a clock.

I have attended minor league games with pitch clocks, and they seem to flow just fine. Short of that, MLB should try offering incentives to move the game along, rather than penalties. Paying the players to play faster likely works better than punishing them for slow play. Then, when they need to take time in an important situation, they can do so without worry.