The Gunners came from a goal down to beat Wigan via a penalty shootout at Wembley to reach the FA Cup final as the club look to end their nine-year wait for silverware
The Gunners appeared to be heading for defeat at Wembley thanks to a 63rd-minute penalty from Jordi Gomez, only for Per Mertesacker to level the scores with eight minutes remaining.
Arsenal went on to win the penalty shootout 4-2 and Vermaelen believes that the triumph will act as a timely boost for Arsenal and ease some of the pressure on Arsene Wenger following a run of poor form.
"There was a lot of talk about needing the result for a few different reasons, for the manager and showing we could fight and I think we did that," Vermaelen told reporters.
"It will give us a boost for the rest of the season now, we can move forward with confidence.
"I'm very happy that we'll go to the final, that's why you play these games of course.
"It was a long game with extra-time and penalties, it's never easy but it's a good win."
Vermaelen was also quick to highlight the showing of goalkeeper Lukasz Fabiani, who produced two crucial saves in the shootout.
"We did have some practices but I wasn't down to take one," he added.
"Lukasz is an outstanding goalie, he works hard for it; he works so hard that he deserves this."