The Latics secured the first major silverware in their 81-year history after Ben Watson's late header sealed a 1-0 victory over Manchester City on Saturday.
Wigan do not have time to savour the achievement as results over the weekend mean that Roberto Martinez's men will be relegated if they fail to defeat Arsenal at the Emirates on Tuesday.
Caldwell believes a string of injuries are partly to blame for the club's precarious position, but remains hopeful that the cup winners can beat the drop if they maintain their Wembley form.
"We know we can be inconsistent. This year injuries have hit us in different spells and have cost us. There's a number of reasons we are where we are," he said.
"We know if we can play like that in the next two games we'll be safe again, and we can try to use this and staying in the league to kick us on to the next level that we're striving to get to.
"And European football as well, which for a club like us is a great achievement. There's a lot to look forward to and next week's going to be another massive week in the history of this club."
Caldwell was hugely impressed with young midfielder Callum McManaman, who claimed the man-of-the-match award in the final, and urged him to play a big role in the last two games.
"I thought he was unbelievable," said Caldwell of 22-year-old McManaman.
"For a young player who's not played a lot of games, to come to an FA Cup final and play against one of the best left-backs in the league in Gael Clichy.
"I thought he caused him so many problems. His ability on the ball is incredible and he's got a big future. Hopefully this can help him kick on as well."