Perch tripped the Spanish goalkeeper, who reacted angrily and head-butted the former Nottingham Forest defender.
Perch went down and referee Martin Atkinson was given little choice but to send Reina off.
Jose Enrique went in goal, as Kenny Dalglish had used all three substitutes, but Alan Pardew didn't want to humiliate the former Toon defender.
United sat back and didn't take a single strike at goal.
Alan Pardew: "I told them to control the game and not risk charging forward.
"And I was pleased the way the players went about it.
"We had a two goal lead and I wanted to keep it."
Watching the game for Sky Sports, TV pundit Chris Coleman said afterwards: "He's an experienced goalkeeper and one of the best in the Premier League. They were 2-0 anyway and he wasn't hurt.
"Get on with the game. If you want to sort something out, you wait until afterwards - you don't go back. As soon as you touch heads with someone, that's that. You're in trouble.
"I think Perch had a very good game at centre-back but I don't like to see that. Maybe I'm old school, but I was brought up taught that even if you are hurt, you get up - you don't show the opposition you're hurt. Nowadays, it seems to be the opposite with a lot of players.
"To go down like that, I don't like to see it. Perch had a great game but he shouldn't be happy with himself for that reaction."
Fellow pundit Danny Murphy: "It was a sending-off. It was a silly kick-out from Perch but I don't know when Reina's reacted like he has.
"Let's not get away from the fact that Reina's at fault though - you just can't do that. You know the rules and you talk about them week in week out with the referees."