Browne saw red for retaliation after a confrontation with Sam Morsy in the 35th minute.
Replays seemed to show that Morsy raised his elbows and caught the Irishman first, with the North End midfielder then punished for retaliation.
Livid Preston boss Alex Neil felt that Morsy was the aggressor and said that the decision of referee Oliver Langford was extremely poor and hard to accept.
Neil continued his protestations after the half-time whistle and was sent to the stands for the second half.
After being on the receiving end of a number of refereeing calls this term - and voicing his displeasure - Warnock was keen to focus on the football on a night when Boro kept in the top-six picture with their second straight home win.
The Boro chief, who substituted Morsy at the break, said: “I have got to do an Arsene Wenger and say it was the least of my worries at half-time and full-time. I have not even seen it.
“I heard them complaining on the bench and what have you, but the referee had a good view in a good position and he thought it was a red card.”
On bringing off Morsy, he added: “I did not like (Paul) Gallagher’s actions against Sam. He’d got a booking and I thought the lesser of two evils was bringing him off because I did not want people winding him up. He was gutted when I brought him off, but he understood.”
Boro took the lead with a fortuitous own goal from Jordan Storey on 22 minutes with the dismissal of Browne ending the game as a competitive contest with the hosts dominating from that juncture.
It was a luckless night for Preston, who scored an offside goal and hit the woodwork before conceding an own goal to ruin a dominant opening.
Substitute Marcus Tavernier - who came on for Morsy at the break - added a second early in the second half, netting a rebound after Chuba Akpom hit the bar.
Warnock continued: “It was difficult. The hardest thing in football - and I know one or two ex-managers have always said to me - is to win two home games on the trot in a short space of time and nothing changes.
“I knew on Saturday when I saw that Preston got beaten at Wycombe that there has got to be a response. It was what we saw.
“But we had some luck and we have not had much luck in the last six months with the first goal. But I thought in the second half, although it is not nice to face ten men, I didn’t think we'd concede anything and I thought the two centre halves were magnificent and I did not think we gave them many opportunities to get back into it.
“I thought we played some good stuff. But it was all about winning tonight and not the performance. We had the performance against Stoke and this was about getting three points.”
The only downer saw Paddy McNair left the fray with a knee injury in the second half.
On what happened, Warnock said: “I don’t know, but it is a strange one around the front of his kneecap, so I am not aware. He knew straight away he had got to come off as he signalled straight away. We will have more tomorrow on that.”