The Spaniard made nine changes from the side that salvaged a 1-1 draw with Fulham on Saturday, but the Premier League strugglers still had too much for their League One opponents and edged to a 1-0 win at Dean Court courtesy of Mario Boselli's first-half strike.
The Cherries hit the crossbar twice but Martinez, who used the additional fixture to once again field a shadow side, was pleased with those who came into the fray.
"The young players and those who needed the minutes showed that they're ready to step up their competition in the squad which is very pleasing to see," Martinez told Sky Sports.
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"An outstanding finish from Mauro Boselli was the difference and in the second half, as we expected, Bournemouth came at us a lot more, but we looked a threat on the counter and were unfortunate not to get a second goal."
Manchester United loanee Angelo Henriquez made his debut, while Roger Espinoza also slotted into the side well on a chilly evening on the south coast.
"They looked comfortable and as though they already have a good understanding with each other and the rest of the team," he added.
"Roger never put a foot wrong, controlled the midfield area with ease and combined his style in possession with an aggression off the ball to win it back, covering the ground well with a real tactical awareness.
"Angelo's acceleration made him a threat throughout the game. His penetrating runs were outstanding and it was unfortunate he couldn't find the back of the net but worked hard for the team.
"The pitch didn't help either team but to see new players come in and perform in such a manner was a real plus."
The result means Wigan now made the short trip to Moss Rose to face Blue Square Premier side Macclesfield Town, who bravely fought back from behind to stun Championship leaders Cardiff City in the third round.
"It's [Macclesfield] going to be a difficult tie," Martinez revealed.
"They deserve all the media attention they get. To beat the Championship leaders is not an easy task."