Gary Caldwell gave the home team the lead, but Wigan were dominated for large periods of the game by a Southampton side that scored second half goals through Rickie Lambert and Morgan Schneiderlin before Shaun Maloney equalised late on.
Martinez admitted that he was impressed by Southampton's play in stopping the effectiveness of Wigan, but took the positives from the one point gained.
"It's a point gained. We knew Southampton would press us and stop us from being on the ball. I feel we accepted that," Martinez said.
"Once we went 1-0 up we played like we had something to lose. We couldn't find space behind them because they were well organised and squeezed high up, pressing very effectively.
"We couldn't be our normal selves. In the second half I thought we defended very well but they had too much of the ball for our liking.
"I have to give credit to Southampton for how they stopped us playing, but we showed incredible character and determination to get back level."