The new signings both netted in the second half to condemn the Shrimpers to an eighth defeat in nine games.
But Fleetwood boss Uwe Rosler was keen to for the whole team to be praised.
“The focus will be on the two debut goalscorers but it was a real team effort,” said Rosler.
“We didn’t give them anything in the first half and then we took our chances on the counter-attack in the second-half.
“We stood firm throughout the game and the longer it went on, our fitness paid dividends.
“Paddy was very good and this is what we bought him for. He gets in the right place in the right time and has great calmness.
“Diagouraga showed his physical presence but he gives us technique as well.
“He has a lot of experience and can run all day long.”
Fleetwood’s win was their fifth in succession on the road and saw them move up to 11th in the standings.
Town came close to breaking the deadlock in the 12th minute when Devante Cole headed Ashley Hunter’s left-wing free-kick against the crossbar from 12 yards.
But Fleetwood broke the deadlock in the 57th minute when a mistake from Southend skipper Anton Ferdinand resulted in Madden teeing up Diagouraga to fire past advancing Shrimpers goalkeeper Mark Oxley.
Fleetwood doubled their lead in the 62nd minute when Kyle Dempsey rolled a pass into the path of Madden, who showed good strength before netting with a well-struck finish.
Southend hit back in the 86th minute with midfielder Michael Kightly scoring a deflected effort from 20 yards but the hosts were unable to net a late leveller, mounting further pressure on manager Phil Brown.
However, he does not fear being sacked despite his side slipping to 18th in the table, just two points above the relegation zone.
“I’ve had a good conversation with the chairman and had a great week too,” said Brown.
“Fifty-five minutes into the game I was still enjoying my week but we were unhinged by a couple of poor mistakes.
“Of course the fans are entitled to vent their anger but the more the players realise we are in spot of bother the more we will be able to get out of it.
“There’s no sense in thinking of the play-offs or anything like that because that’s gone at the moment.
“We need to knuckle down and work hard because we’re in a spot of bother right now.
“I’m fully to blame for what’s going on.
“I’m letting the players down and they’re letting me down too but I very much believe we will turn things around.”
Morecambe have no fresh injury concerns ahead of Tuesday's Sky Bet League Two home clash with Colchester.