Preston tried and held on till first half which ended goalless unfortunately fell in the second half as the team couldn't hold on as they conceded four goal in the second half Chelsea, no doubt is the better side having dominated the match with 70% possession and 12 shots on target against the championship side, remember FA Cup is usually synonymous with upset I believe Chelsea was a bit cautious not to concede against Preston they are frustrated in the first half, though you are worried about Chelsea sluggish style of play but I believe that would change with time because Pochettino hasn't gotten a real first eleven squad yet and once the team clicks they would be unstoppable.
In the first half, Chelsea were not very persistent and indeed this result was not surprising because in terms of quality Chelsea were much better and they deserved to win with a convincing score.
I think what happened in the first half is not a significant problem because what is needed is the final result and Chelsea won as predicted, there were no surprises in this match.