West Brom took the lead in the 31st minute when James Morrison powered home a header from inside the six-yard box after Chris Brunt's cross from the left, and they doubled their advantage shortly before half-time when Gary Caldwell could only turn Billy Jones' cross-shot into his own net.
Arouna Kone immediately reduced the arrears ahead of the interval, tapping home from point-blank range at the far post following Jean Beausejour's dangerous low cross but it took a wonder-save from Ali Al-Habsi to deny Romelu Lukaku a third after the break.
Wigan went into the game following back-to-back victories over West Ham and Tottenham, but were unable to record a third successive Premier League triumph.
Martinez said: "I don't think we were as good as we can be today and that is very frustrating. We know that West Brom are a really strong unit who play with real confidence.
"To concede two goals early on in the game was really disappointing. When you are playing against a side like West Brom the priority is to score the first goal.
"Allowing them to have two goals gave them a real cushion. Our movement wasn't as sharp and our quality in the last third was affected by the two goals we conceded. We did get frustrated.
"We wanted to win so much after the two great results we had. We didn't expect to go two goals down and I don't think we could cope with that as well as we wanted to.
"It wasn't our day. I don't think we were lucky enough to get a positive result today."