Midfielder Jordi Gomez was sent off two minutes into the second half at the Stadium of Light for a lunging challenge on Black Cats full-back Danny Rose.
Webb, who took charge of the 2010 World Cup final, immediately showed him a red card and Sunderland took full advantage within four minutes when Steven Fletcher scored the game's only goal.
Martinez, who is facing an FA charge over comments he made on Michael Oliver's handling of his side's 4-0 defeat by Manchester United earlier this month, felt the dismissal was harsh, and insisted that if Gomez had to go, so too should have Sebastian Larsson for a challenge on Arouna Kone later in the half which went unpunished.
He said: "I think it's harsh. It's harsh because Danny Rose loses the ball slightly.
"Jordi tackles as a striker tackles, showing the studs, but he never leaves the ground, it's not a two-footed challenge.
"I can understand why the referee gave it, but I think it's very, very harsh.
"My disappointment is that Larsson has made a worse tackle against Kone and is not even shown a yellow card.
"That's just as you want as a manager, you want consistency for both teams.
"It's down to the referee's decision if he considers that that challenge is a red card, but then every challenge in the same manner should be a red card.
"That's the disappointment. At the moment, we are on the back of a few bad decisions and you just need to take it in football. It happens.
"You just hope that over the course of the season, you are going to get good calls coming in our favour even though now, we find it difficult to understand that's going to happen."
Opposite number Martin O'Neill admitted that the sending-off had changed the game, but was not convinced Webb had any other option.
He said: "My first thought was it looked a bit harsh to begin with. Having seen it back, I'm not so sure that the referee had much alternative.
"I was the first one to say on Tuesday night that Lee Cattermole deserved to be sent off.
"Whether Roberto agrees or disagrees with it - it may have been a sending-off - but I think his main point was that maybe it changed the dynamic of the game from that viewpoint because we reaped our reward pretty quickly.
"We scored soon after that and it gave us some impetus, a lot of impetus, in fact."
Wigan enjoyed the better of the first half with Simon Mignolet having to make early saves from James McCarthy and Kone, while McCarthy fired just wide two minutes before the break after Ivan Ramis had hacked a Larsson free-kick off the line at the other end.
However, the game changed two minutes after the restart when Gomez departed, and Fletcher cashed in when he turned home James McClean's driven cross to claim his fifth goal in four Barclays Premier League game.
The Scot's strike was enough to end a run of 12 league games without a win, and O'Neill was delighted.
Asked if his £12million summer signing was proving a bargain, he replied with a smile: "I agree, yes - £35million without a problem, and add-ons.
"He did very, very well. He was brilliant today for us. Wigan came and played their part, and I have to thank Mignolet for making two incredibly good saves for us to keep it at 0-0.
"Fletcher has come up big again for us, so eventually we have won the game, although it was edgy towards the end. But the win was vitally important for us and it keeps us going."