The League One side took the lead through Eunan O'Kane just before the break but the Latics clawed their way back into it when Jordi Gomez equalised after initially seeing his spot-kick saved.
And Martinez believes a replay is no more than the Cherries deserved for a confident display against the Premier League strugglers.
"It's no coincidence that they've had a 16-game unbeaten period," said Martinez.
"I thought they were really well organised. They played with really good tempo and off the ball they worked extremely hard.
"And on the ball they tried to play, get the ball wide and they had good pace in the team so overall I thought it was a really good Bournemouth side."
Martinez selected a youthful side, sparking claims he had disrespected the competition, but felt the development of the players was key.
"From our point of view, when you make nine changes it is going to take a bit of time to get the partnerships knowing each other," he added.
"But I thought overall we controlled the game very well and I was pleased with the youngsters, especially Roman Golobart who had a faultless performance.
"We've spent a lot of money on the youth facilities and if we are going to do that we need to be brave enough and patient enough to give them opportunities.
"I thought everyone showed they were ready. In the second half we had a few chances but overall I do think Bournemouth deserved a draw."