The much vaunted Australian team, led off by 100 metres freestyle gold medal favourite James Magnussen, were expected to challenge with the Americans for the title on Sunday but ended up fourth as France shocked everyone.
"I've had a long time to think about it because I didn't get any sleep last night," Targett, who swam second behind Magnussen's disappointing 48.03 second opening leg, told a news conference.
"It didn't go to plan, we had a plan to establish a lead then building on it and that didn't go to plan.
"We thought we could do something very special and, as you can see, we fell well short," he added.
World champion Magnussen has by far the fastest time of the year in the 100 metres freestyle (47.10 seconds) and was expected to end a 44-year drought for Australia in the individual event as well as spearhead the relay.
Australia's plain-speaking head coach Leigh Nugent described the relay race as a "disastrous result", a sentiment Targett was inclined to agree with.
"We, like everybody else, expected to come home with gold or at least finish on the podium but it went more than slightly wrong and I'm sitting here without a medal around my neck," he said.
"I personally was happy with my swim and I'm not going to comment on others, obviously nobody expected James to swim a 48 and I think that may have thrown us off mentally."
Magnussen, noted for his oft-articulated confidence in his own abilities, took something of a battering in the Australian media on Monday, particularly for sitting down rather than standing with his team mates as the race was played out.
"I honestly can't remember a whole lot about the race, I know he was sitting there in a state of shock," said Targett.
"To tell you the truth, that was probably the last thing on his mind.
"I can't speak for him but we're still acting as a team right now and when I see James again, he knows he'll have my full support. Hopefully, I'll have a small part in his bounce back."
Targett said he did not think Magnussen's disappointing relay would necessarily give confidence to his rivals in the individual event.
"It's however they want to interpret it, they know he still has the potential to go 47.1 and they can't say that," he said.
"Unfortunately for them, there's nothing they can do to effect him, he's going to have to bounce back and I really do hope he does."
Asked whether Magnussen could still shine in London, Targett was unequivocal.
- James Magnussen