The R's held the lead at the break thanks to a goal from debutant Loic Remy.
However, Joe Cole equalised after the restart for the Hammers, who then put Redknapp's team under a lot of pressure in the closing stages as they went in search of a winner.
QPR held firm though and Redknapp admitted that he was pleased with the result.
"We got 1-0 up and looked okay at that stage. I felt we looked like we had more goals in us on the counter-attack with Remy and his pace, and Adel Taarabt playing in behind," he told the club's official website. "But then we started giving the ball away, came under a lot of pressure and dropped deeper and deeper.
"In the end we were under pressure and found it very hard to get out, it was difficult.
"We fought for our lives and we'll take a point. That's five games unbeaten, that's a big improvement."
Redknapp's men are still bottom of the Premier League table and are five points from safety.