The north London outfit trailed 2-0 after just eight minutes at Wembley, before Aaron Ramsey's goal in extra-time finally saw silverware delivered to Arsene Wenger's side.
Podolski was on hand to douse Wenger in champagne, and the Germany international - who has previously had success at Bayern Munich - said savouring the achievement was important.
"He needed it. After nine years, he needs a little drink, of course. When I played for Bayern, I won the league title and the cup," he said.
"When you win something you must celebrate. You celebrate, then you focus on next season.
"When you wait nine years, especially for the fans, it's something special.
"Everywhere there was pressure about Arsenal winning nothing, the newspapers were crazy.
"Now we have this done. Nine years is done and we have the cup."
Podolski said securing trophies was vital for a 'big club like Arsenal', despite Wenger staying on for the duration of the club's drought.
"When you play for a big club, the focus is always on the title and the Champions League, the FA Cup and the League Cup, everything," he said.
"When you are at a big club like Arsenal you have to focus to win a trophy every year. This year we have got the trophy and it's important for us.
"When you finish fourth, it's not easy. We lost to the teams ahead of us: Chelsea, Man City and Liverpool.
"These are the matches we must focus on next season. We win the two matches against those and we win the title.
"We don't need a lot. Every year, players come and go. This is football. But I'm happy at this club."
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