The Gunners are set to go head to head with Chelsea after Alexis Sanchez's extra-time winner saw his side come from behind to seal a return to Wembley in May.
Victory comes as blessed relief for Wenger who, following a dismal run of form both at home and abroad, has faced increased calls to walk away at the end of the season.
And midfielder Ramsey says the team feel an obligation to go one better for their beleaguered boss.
"It was important for us to get to the final for him, for ourselves and for the fans, and have a bit of positivity around the club," he said after the match.
"He was over the moon for us but we are delighted as well that we have got to a final for him.
"I think he deserves that and hopefully now we can kick on and win it for him.
"We have seven cup finals now to try to finish off the job and get that Champions League place, then hopefully we'll have something to celebrate at the end of the year."