Queens Park Rangers won in the Premier League for the first time this season, beating Fulham 2-1 at Loftus Road on Saturday.
Two second-half goals from Adel Taarabt secured the victory, despite a late Mladen Petric strike that brought the London derby to life.
''We deserved it, we were the better team,'' said Redknapp, who had seen his new side draw each of his first three games in charge. ''It would have been a travesty if we'd conceded in the last couple of minutes.
''If we hadn't have won today, it would have been absolutely desperate.''
Taarabt opened the scoring in the 52nd minute with a shot from outside the area that deflected off Fulham defender Brede Hangeland. He doubled the advantage in the 69th when he received the ball just beyond the halfway line, wafted past the Fulham defenders, before poking the ball past Mark Schwarzer in the visitors' goal with the outside of his foot.
Petric's deflected effort from outside the box in the 88th minute beat QPR keeper Robert Green, but Fulham couldn't find the equalizer.
''I'm very disappointed,'' said Fulham manager Martin Jol. ''I can't complain about the goals. In the first half, we never got the ball to our quality players.
''We couldn't do the simple things; we couldn't play in a flow.''
QPR dominated the first 45 minutes. The first clear chance of the game fell to Jamie Mackie after eight minutes. The Scottish midfielder anticipated John Arne Riise's header back to Schwarzer, but lacked the composure to finish, putting the ball wide from six yards.
Taarabt hinted at his goal-scoring potential throughout the first half, threatening the Fulham defence with skillful dribbling. He eventually forced the breakthrough in the 52nd minute when he ran at the Fulham defence with few options and shot from outside the area.
Schwarzer was likely to have saved his effort, but a deflection from captain Hangeland took the ball away from the Australian goalkeeper.
It was the second deflected goal in a week that had beaten Schwarzer after Newcastle's Hatem Ben Arfa's shot took an even bigger deflection on the way into his net on Monday.
In the 69th minute, Taarabt capped an excellent individual display with a fine individual goal. Receiving the ball at the halfway line, he ran past Fulham's defenders before picking out the bottom corner of Schwarzer's goal, giving the keeper little chance.
''Fantastic ability, amazing talent,'' said Redknapp of man of the match Taarabt.
Fulham's consolation goal came when second-half substitute Petric found the bottom left-hand corner of Green's goal, his shot deflecting off Alejandro Faurlin's boot.
Both teams threatened to score again with Djibril Cisse coming closest when his header was clawed away from goal by Schwarzer but the scoreline stood.
The win lifts QPR off the bottom of the table to 19th with 10 points. Fulham remains 13th with 20.
