The German forward was taken off in the 68th minute at Wembley as Arsenal secured a place in the final with by beating the holders 4-2 on penalties.
That substitution marked the 12th time this season that Podolski has failed to complete a full 90 minutes, and the former Bayern Munich man is disappointed with the way he has been deployed by manager Arsene Wenger.
"I play and in the last games, I always come out and of course you cannot be happy when you always go out after 60, 70 minutes," Podolski told reporters.
"When you go out and you are happy, you are not a footballer so of course I am not happy always to be substituted.
"It's the decision of the boss, he is the manager. He decides who comes in, who comes out, who are the first XI.
"It's not always easy when you play for a big club but of course I am not happy to always come out and watch from outside. You cannot be happy with this situation."
Victory in the FA Cup would secure Arsenal's first major trophy since they last won the competition in 2005, although they are in danger of missing out on the UEFA Champions League after Everton moved into fourth place with a 1-0 win at Sunderland on Saturday.
And, ahead of Tuesday's clash with West Ham, Podolski conceded that failure to finish in the Premier League's top four would be a disaster for Arsenal.
He added: "Every season is a pressure when you don't win anything and the newspapers speak about it, the fans gets nervous but we have the chance this year to win the FA Cup so maybe it helps the club, us and the boss.
"But the other important thing is to get fourth place back because when you don't play in the Champions League, it's a disaster."
