Is it acceptable to pair a player with the same colour three times in a row? A few months before an official national tournament is held, an announcement is published, which contains information about specific rules (e.g., no draw offers until the 30th move), etc. One thing that caught my attention was that a player can't have the same colour for 3 consecutive rounds.
Yet, in the last round, I played Black and my opponent White. After the end of the game, I realize that my opponent had taken White 3 times in a row. Swapping colours was also impossible since I was Black in the last 2 rounds.
Can the result actually be changed? Or should the game be replayed?
As I am not an arbiter, I'd also like to ask whether there is an option in Swiss Manager (the pairing program used) not to allow players to get the same color 3 times in a row?
Lodging an appeal also came to mind that time. However, can the result
  actually be changed?


No. Only in extreme cases such as cheating can the result be changed.


  Or should the game be replayed?


No. There is no reason why the game should be replayed.


  In addition, as I am not an arbiter, is there an option in Swiss
  Manager (the pairing program which was used to make the pairings) not
  to allow players get the same color 3 times continuously?


Swiss Manager uses the JaVaFo pairing engine written by FIDE. The pairing engine implements the FIDE defined pairing rules. As far as I know (I am a FIDE arbiter) the only pairing rule that can be overridden is the one which says that a player who has already had a voluntary bye can also be given a compulsory bye in a later round given an odd number of players. In my experience this is never done.


  In the last round, I played with Black and my opponent with White.
  
  After the game, which I unfortunately lost, due to the lack of opening
  preparation, I realized that my opponent had taken White 3 times in
  the 3 last rounds. Playing with opposite colours was also impossible,
  since I had White 2 times continuously. In addition, I had played with
  most of the players which were up to the 10th position, so I couldn't
  find anyone else to play - maybe this is an exception?


In the FIDE Handbook the rules for Swiss pairing are given in the section Basic rules for Swiss Systems. 

Your case is covered by these two rules.


  f For each player the difference between the number of black and the
  number of white games shall not be greater than 2 or less than –2.
  Each system may have exceptions to this rule in the last round of a tournament.
  
  g No player shall receive the same colour three times in a row.
  Each system may have exceptions to this rule in the last round of a tournament.


In the last round of a tournament the requirement to allow the highest placed players to play each other in the interests of having clear winners and major places decided fairly takes precedence over most of the other rules. The rule which says that two players who have already played in an earlier round cannot be paired against each other again takes precedence over all other rules and cannot be broken.