But Attwell - the Premier League's youngest ref - appeared to be spot on with both decisions as the Hammers consolidated seventh spot in the table.
Goalscorer Cole went after 37 minutes after collecting his second yellow of the night, while midfielder Cattermole was shown a straight red on 54 minutes after cutting down Scott Parker, who infuriated the home fans by making a meal of it.
Wigan - now without a win in the last eight matches - had Mido and Antonio Valencia back after injury, with Ben Watson among the subs after his one-game ban.
West Ham were missing Swiss midfielder Valon Behrami, the latest addition to an already lengthy casualty list with a damaged knee from Saturday's win over Manchester City.
Keeper Robert Green was twice forced into early action dealing with free-kicks from Egypt strikers Amr Zaki and Mido.
Both managed to beat the wall but Green reacted well to turn Zaki's shot round the post and did even better when Mido cracked in a powerful low shot.
Green failed to hold onto it but recovered superbly to get it away before Luis Antonio Valencia could pounce on the rebound.
David Di Michele hammered one wide for the visitors and Cole should have made more of a good chance when he raced into the Wigan area but was squeezed out by Chris Kirkland and Emmerson Boyce.
But the Hammers took the lead on 34 minutes with a classic strike from Cole, who curled the shot beyond Kirkland for his 11th of the season after a terrific build up involving Parker, Di Michele and Mark Noble.
But three minutes later, Cole was sent off after he appeared to go high on Boyce.
Skipper Parker had to be kept apart from Michael Brown, who was also cautioned for his reaction to the Cole incident.
When tempers had cooled, ten-man West Ham enjoyed a bit of luck when Mido headed against the post from Valencia's cross and then Cattermole fired just wide with another attempt on goal.
The Latics had another chance on the re-start when a Valencia corner flashed across goal but Titus Bramble could not come up with the finish at the back post.
With both sides down to ten after Cattermole's sending off, Noble was just inches away from a second for the Hammers, who suffered another injury blow when Jack Collison was stretchered off.
But the visitors successfully played out time to further boost their chances of securing UEFA Cup football for next season.