The Black Cats surrendered almost total control of possession and resorted to a smash-and-grab approach against the league leaders, who had won their previous six Championship games.
Despite their backs-to-the-wall display, Sunderland earned a deserved point courtesy of a steely showing that saw them prevent the league's highest scorers from having a shot on target until the 73rd minute.
And Coleman - in charge only three weeks - insists that such dogged defensive displays are a necessity if Sunderland are avoid back-to-back relegations and drop into League One.
Coleman keen to continue slow but steady progression
"The early signs are okay," the Welshman said. "Last week, the expectation was to win that home game and we fell flat on our face. Again step by step, game by game, we've got to keep building.
"It's all from the training ground. Every success comes from there, it's diligence, resilience and grit, all those nasty words; accountability. The better you get, the better results you get.
"When I first came, I don't have a magical way that no-one has ever seen before. But I know to mould a team and organise a team. I need to know that otherwise going forward we'll be exactly as we are."
Coleman was forced into two changes due to suspension and injury but dropped midfielder Aiden McGeady for Donald Love as he opted for a defensive-minded 3-4-3 set-up.
He continued: "I will change it up. I will change the system. Sometimes when they're playing well, sometimes when they're not.
"It's about everybody and they have to understand that. Maybe next Saturday the team and the shape will be different again. We'll look at that.
"We went with the shape and personnel we thought was best to face the opposition. It maybe different next week, whether it's Aidy being rested or Catts or whoever, it's not personal to them. It's horses for courses."
"I don't care if we have to play ugly"
Wolves' attacking riches had saw them score 41 goals and win 16 matches in their first 20 league games, but they drew a blank when faced with the sheer numbers that Sunderland packed behind the ball.
And while Coleman admitted his side's style was far from easy on the eye - managing a single shot all game - he declared it essential that they first ensure they are solid at the back in order to climb the table.
"We need that platform," he said. "We're not going to win games 5-4 and 4-3 every week. Wolves might because you see the players they've got.
"They've spent a hell of a lot of money on offensive players who are fantastic at this level and they're going to score a lot of goals.
"We may have to win 1-0 and to do that we have to learn how to keep a clean sheet. Sometimes that means playing ugly but I don't care about that, I care about getting results.
"That's all we can do, the very least we can do, is battle. From the start I've said if we don't do that, what is there?
"The buzzwords now are playing between the lines and creating overloads but we need to be hard to play against which means we end up getting better results. That's it."
Coleman admits desperate need for Stadium of Light win
Coleman also acknowledged the need for a long-awaited win as his side look towards a clash with Fulham next weekend at the Stadium of Light, where they have not won in several days shy of a year.
"This is another step forward for us. We've got a lot of hard work ahead and a long way to go but I'm proud of the team.
"We've got to keep proving that there is spirit and there is harmony and we did that. I've seen good signs but we have got to keep doing it. We must look to have the same spirit next weekend even though we're at home.
"The fans are super unhappy and I can't blame them. We have to show that same grit and resilience at home and be brave. No matter what we have to do to find the results at home, we'll find the answers and make sure we do.
"We need to win 1-0 at home. I don't care if it's ugly; if it's swashbuckling football, fantastic. If it's 3-0 or 4-0 or if we win 1-0 and it's a controversial goal, I couldn't care less how it comes.
"I said last week when we lost, we can talk as much as we like about what's going on outside of the club, but we need to put a smile on everybody's face and that means winning a home game.
"Next week will be just as hard as this week but we'll have the psychological factor of this."