The visitors sealed their place in the last 16, two minutes from time, when substitute Hal Robson Kanu headed home from six yards.
Kenwyne Jones had given Cardiff the lead with a smart header from Peter Whittingham's 25th minute corner, before Oliver Norwood levelled after 64 minutes with a free-kick from 25 yards.
Cardiff City 1-2 Reading
The FA Cup
Fourth Round Proper
3pm, Saturday 24 January 2015
Cardiff City Stadium
Winners receive £90,000 from prize fund
Reading dominated the game for all but a short period in the first half and were good value for the win. In contrast, it was not such a good day for Cardiff for whom this was a third successive defeat in eight days.
Clarke said: "I'm pleased with second half as I thought we let ourselves down in the first half. We tweaked the system but more importantly we tweaked the mentality. We got Nick Blackman further forward and it helped and we were on the front foot. I thought we expressed ourselves in the second half and deserved to get the win.
"We were a little bit sleepy in the first half and waiting things to happen, but then we forced themselves on the game and they did what I like to see for my team.
"It was just a quiet chat at the interval to put one or two things right and reminded them of their responsibility to the marvellous travelling fans.
"Hal did what I asked him to do. I asked him to have an impact and he did exactly that.
“Everyone will be thinking it [The FA Cup] has opened up a bit, especially with Chelsea and Manchester City out. But we won't get carried away with it.
"It is certainly a better feeling than when I last came down here," quipped Clarke, who was sacked by West Brom after they lost 1-0 to Cardiff, in the Premier League, in December 2013.
"I certainly don't think the chairman will be waiting for me in the car park tonight. Mind you, I didn't think he would be waiting in the car park for me that night."
Cardiff manager Russell Slade was desperately disappointed with what he saw as his side's worst 45 minutes since his arrival at the club.
He said: "In the second half, it looked like there was only one team who was going to push on and win it. I am very disappointed with our second half performance.
"They put us on the back foot in the first 15 minutes of the second half and we found it very difficult to string two passes together.
"We should have defended the free-kick better. However, that got them back into the game and they went on to win it. Obviously as the manager I take full responsibility.
"I thought we were devoid of energy and ideas and it's the most disappointing 45 minutes we have had since I've been here.
"It's very often not just one thing, but a few things, that go wrong. For example we didn't do enough to affect the ball that came into the box for the winning goal. They had one player in the box and we had six.
"If I was in the crowd in the second period I would probably have walked out myself. Today is a bad day for us and it looks as if we are taking a step in the wrong direction.
"But we have to face the criticism, we have to unite and we have to be strong. We have to respond, that's the only thing we can do.
"It just happens that our next opportunity is probably one of the toughest games in the calendar.
"It is going to be a busy week for the football club and there could be one or two leaving and one or two coming in."
Cardiff City (4-4-2): 33 Simon Moore; 3 Fabio Da Silva; 36 Sean Morrison, 6 Ben Turner, 4 Scott Malone; 40 Kadeem Harris, 17 Aron Gunnarsson, 7 Peter Whittingham, 11 Craig Noone; 9 Kenwyne Jones, 29 Alex Revell.
Substitutes: 16 Matt Connolly for Turner 42; 18 Tom Adeyemi for Revell 71; 14 Federico Macheda for Harris 84
Substitutes not used: 42 Ben Wilson, 12 Declan John, 21 Joe Ralls, 45 Tommy O'Sullivan
Goals: Kenwyne Jones 25
Reading (4-5-1): 1 Adam Federici; 2 Chris Gunter, 5 Alex Pearce, 15 Michael Hector, 11 Jordan Obita; 12 Gareth McCleary, 6 Oliver Norwood, 14 Nathaniel Chalobah, 23 Danny Williams, 22 Nick Blackman; 7 Pavel Pogrebnyak
Substitutes: 3 Stephen Kelly for Gunter 35, 9 Hal Robson-Kanu for Blackman 82, 35 Jake Cooper for Norwood 88
Substitutes not used: 31 Mikkel Andersen, 10 Simon Cox, 21 Jem Karacan, 25 Jake Taylor
Goals: Oliver Norwood 64, Hal Robson Kanu 88
Referee: Lee Probert
Watch the highlights from the Cardiff City Stadium