However, the striker made amends in impressive style in the 34th minute when he provided the finish to a slick passing move.
Parker slid the ball into David Di Michele who exchanged passes with Noble before playing in Cole on the left of the penalty area and the striker opened his body before curling a shot beyond Kirkland and into the far corner of the net.
Just three minutes later, after Parker had been booked for raking his studs down Michael Brown's shin, Cole got himself sent off.
His raised foot as Emmerson Boyce went to head the ball could have been construed as dangerous and Attwell produced a second yellow card and then a red, which then sparked a small confrontation between Parker and Brown which saw both cautioned.
Wigan pressed for an equaliser and in first-half stoppage-time Mido headed Charles N'Zogbia's left-wing cross wide.
Neill, who rode his luck in the first half, was booked in the 49th minute for going over the ball and into Cattermole.
The Wigan midfielder then pressed the self-destruct button two minutes later when he jumped into the back of Parker and was shown a straight red card.
Despite going down as though he was seriously injured, Parker was able to walk off the pitch and seemed to suffer few after-effects, but he did little to endear himself to the home fans when he appeared to make a spitting gesture towards the crowd behind the dug-out.
Valencia was next into Attwell's book for obstructing Herita Ilunga in the 60th minute.
Wigan's next chance again fell to Bramble after Boyce and Mido had knocked down N'Zogbia's corner but he blazed well over.
With 14 minutes to go, Jack Collison, under no pressure from anyone, collapsed in agony as he tried to control the ball on the right touchline.
Jonathan Spector was brought on to replace him while the youngster was still receiving treatment and he eventually departed on a stretcher with his right ankle strapped up.
He was the second West Ham player to leave the field in such circumstances in successive matches after fellow midfielder Valon Behrami sustained a serious knee injury on Sunday.
Valencia had a long-range effort saved by Green and Hugo Rodallega's overhead kick went wide as even six minutes of added time were not enough for Wigan to grab an equaliser.