Redknapp was keen to bolster his forward options at Loftus Road, but Toronto FC wanted to keep Defoe for their MLS playoff run and terms were not agreed with Borini.
The Liverpool striker was linked with a move to Sunderland but, as the deadline approached, QPR emerged as favourites and entered talks with the Italian.
But personal terms proved a stumbling block and Redknapp told Sky Sports that he was disappointed he was unable to make a third or fourth signing of the day after bringing in Sandro from Spurs and Niko Kranjcar on loan from Dynamo Kiev.
"Jermain wanted to come," Redknapp said. "We were hoping to get him. We agreed a deal with Toronto but it was difficult for them to release him.
"They are looking to get in the playoffs and we didn't want to disrupt their club or anything else so we moved on.
"Borini, we just couldn't do a deal with the player. We agreed a deal with Liverpool but we couldn't meet what the lad was looking for."