The 26-year-old, who made his 24th appearance this season for the Latics, grabbed the opener before Dan Burn and Callum Elder strikes sent the Cherries packing.
"It was a fantastic performance and when you think of the players who were left out of the team as well it’s just incredible," Morsy told the club website.
"The lads who came in were brilliant and the lads who came off the bench were superb. They’re the lads who deserve real credit.
"We wanted to give the fans something to shout about because we haven’t scored in our last few home games. We believe in our style and have always had a strong base, but maybe the last couple of games we’ve just lost that little spark so to score three tonight is fantastic."
On his opener, he said: "Anthony Barry, the first team coach practices those sort of situations with us every day, so when I get in those positions I feel confident because of the repetition.
"You can never be too confident because we were 2-0 up at their place and ended drawing 2-2, but defensively we were superb tonight and were delighted to keep a clean sheet. Jamie Jones was brilliant and made a couple of great saves."
Ahead of the fourth round showdown with West Ham, Morsy believes they can replicate their good show to silence David Moyes’ men on January 27.
"West Ham have got some real top class players and it’ll be a massive game for us. The club has obviously got big history in this competition so let’s see what happens in the next round.
"The league is our priority but we want to do well in the FA Cup too because games like this are the ones you want to play in. A lot of the teams we play in the league are happy to sit back and soak up the pressure, but teams like Bournemouth and West Ham come and have a go which is great."