Will Grigg's 79th-minute goal gave Paul Cook's League One side a remarkable upset triumph, ending City's hopes of an unprecedented quadruple in the process.
Guardiola was involved in a heated exchange with Cook as tempers also boiled over on the field following Delph's rash lunge on Latics midfielder Max Power during first-half stoppage time.
The City boss, who has urged officials to protect players from dangerous tackles after seeing his men on the receiving end over recent weeks, described the challenge that will rule Delph out of Sunday's Carabao Cup final against Arsenal as "unnecessary".
Asked for his thoughts on the incident at a post-match news conference, Guardiola replied: "Red card. It's a red card, yeah.
"For me it's an unnecessary action and the referee decides when he decides. It can be a red card. We have to learn about that."
Guardiola was keen to dismiss any notion of lingering animosity from the touchline row, which he claimed stemmed from telling Cook to remain in his technical area.
"Nothing, just [saying] 'stay in his position'. That's all," said the Catalan, who quickly tired of questions on the subject.
"Guys, if you want to ask me about football, ask me about football. Nothing happened in the tunnel, nothing happened with my colleague. Nothing.
"It was just 'please stay in your position'. That's all."
Claudio Bravo was brought in for his now customary appearance in goal for City's domestic cup ties, while Nicolas Otamendi and Raheem Sterling were rested.
It was otherwise a very strong City side that Wigan overcame, but Guardiola had no complaints over his team's efforts.
"I judge my team for the intentions, not for the results," he added. "The intentions during the season, even today, were good.
"We tried, 10 against 11, we created chances. Their keeper was good, we could not finish. Mentally it is hard fighting in four competitions and we did it.
"The intentions were good and, after that, the result speaks for itself. 1-0 — congratulations to Wigan. Normally when I lose, my first words are always for the winner.
"It [defeat] happened against Liverpool, it happened today, it will happen again. Congratulations to Wigan, all the best for the future."