Cattermole, the former Latics midfielder who was captaining the visitors at the DW Stadium on Saturday, was shown red by referee Andre Marriner midway through the first half after being booked twice in quick succession for fouls on Mohamed Diame and Hugo Rodallega.
Sunderland went on to take a 66th-minute lead through Asamoah Gyan's debut strike before Antolin Alcaraz's late equaliser and Martinez was delighted with the way his team handled the situation.
"The sending-off really made things difficult for ourselves," Martinez said.
"All of a sudden Sunderland don't have to think, they know exactly what they have to do - get behind the ball and play that role and they did that extremely well.
"We were the ones who had to find solutions, create chances and take risks to take control of the game.
"We did that exceptionally well in the second half without reaching the level that we can reach in possession."
After Gyan, Sunderland's record signing, was introduced to the action by replacing Danny Welbeck at half-time, Martinez brought on two new recruits of his own in Franco Di Santo and Tom Cleverley.
Charles N'Zogbia, left out of the Latics' previous match at Tottenham following the breakdown of his proposed transfer to Birmingham, also made an appearance from the bench and Martinez praised the impact of his substitutes in helping the hosts salvage a draw.
"It was very important and exactly what you need from a player that comes off the bench," Martinez said.
"We were looking at Franco for the first time, playing with his new team-mates, Tom Cleverley, who had a real good arrogance and understanding of the game straight away, and Charles N'Zogbia, who looked as committed as he has always been and someone who really creates problems for the opposition.
"I am very happy with the squad we have assembled. It is clear there is still work to do and we are still a team that needs to gel.
"We need a little bit more experience and to develop that know-how.
"With the (Sunderland) goal, we didn't sense the danger quick enough and we allowed world-class talent to get on the end of a very good ball, but that is where the work is.
"Overall, having that togetherness and desire to work for each other and the talent to unlock a defence like Sunderland's, who got men behind the ball - that for me is the real positive from this game."
Sunderland manager Steve Bruce had "no complaints" about Cattermole's dismissal and felt the Wearsiders had been unlucky not to come away with all three points.
"I just hoped we were going to hold on but it wasn't to be unfortunately," Bruce said.
"But it was a great effort from them. To be at 10 men from 20 or 25 minutes, it was a great effort.
"I thought the goalkeeper and the back four in particular were terrific so it's a shame we couldn't hang on and with the form the goalkeeper (Simon Mignolet) is in, it has taken a horrible deflection to beat him."