Blues bossed the first hour at the DW Stadium, but they had to dig in for the final third to earn a point from a goalless draw after Lingard was sent off by referee Stephen Martin for a lunge on Jordi Gomez.
The on-loan Manchester United man clearly felt he had been fouled by Chris McCann moments earlier, only for the official to wave play on.
And Clark admits it is just part of the learning curve for the youngster.
"Being brutally honest, I was initially questioning the fourth official as to why we hadn't been given the free-kick in the first place," Clark said.
"As I turned back, Jesse was coming out of the tackle and their lad was on the deck.
"Judging by the boy's reaction in the dressing room - he hasn't questioned the decision, he hasn't said it wasn't a foul - it looks like he's lost his head for a few seconds and it's proved costly.
"We've all been there, it's a very passionate game, it's understandable. In the heat of the moment the red mist can descend on you.
"He would have felt an injustice at not being awarded the foul, and he's obviously over-reacted.
"He's such a young boy, his enthusiasm is brilliant. But he's just got to make sure that when he doesn't get a decision he keeps his composure."
Clark is also keeping this fingers crossed that he has not seen the last of Lingard - whose loan from United expires next week - in a Birmingham shirt.
"We're just hoping this isn't his last game for us," Clark added.
"He's been terrific for us but he'll pick up a three-match ban now and his loan will expire in the middle of that.
"I tried to put some earmuffs on the other day when I heard David Moyes talking about bringing some of his loan players back to Old Trafford.
"Hopefully I can persuade David that the best thing for Manchester United is that his development will be better served here.
"We can promise that he will be playing all the time - as long as he's not suspended!"
Clark was otherwise delighted with his side, who extended their unbeaten run to eight matches.
"There was only one winner in the first half. Wigan never gave us any issues at all," the Birmingham boss insisted.
"Even when we went down to 10 men, our goalkeeper's not had to make many saves. With 11 men against 11 we were certainly the dominant team."
Uwe Rosler was happy with a point despite losing his 100 per cent league record as Wigan boss.
The German had presided over back-to-back wins over Bolton and Reading - as well as seeing his side thwarted by the weather at Sheffield Wednesday last week when they led 1-0.
But he had no complaints after seeing his side fail to score for the first time under his stewardship.
"I was certainly not disappointed with a point," Rosler said.
"You all saw the game. Sometimes you have to accept that you don't have enough on the day to win the game.
"Birmingham made it very difficult for us, and 11-against-11 we would have found it very difficult to get anything.
"I thought we started okay for the first five or 10 minutes, you saw what we wanted to do.
"Then we had some very nervy moments when we lost the ball in stupid areas and you saw the confidence levels drop.
"Our pressing football didn't work at all, and that was a big part of our game-plan.
"The red card helped us but we never really had any clear-cut chances. But that is football."
Rosler also confirmed Nick Powell, another youngster on loan from Manchester United, missed the game through injury.
"Yes, he was injured," Rosler added. "He is our top goalscorer, I wouldn't rest him. We are not in that position."