"We had them on the ropes and didn't finish the job," said Saker.
The Analyst: Perth's extra bounce
"It's partly down to the way they played with the bat, but we didn't deliver what we should have done."
Australia's recovery in Perth mirrored they way they fought back to earn big victories in the opening two Tests of the series.
In Brisbane they stumbled to 132-6 on day one before recording a 381-run win, while in Adelaide the 218-run success came after they slipped to 174-4 batting first.
"There's no doubt we let it slip - and probably not for the first time this series," added
47-year-old Saker, an Australian
who joined the England set-up in 2010.
"The disappointing thing is I think we did chase wickets, and that's probably one of the first times we've done that as a group for as long as I've been in charge."
At 2-0 down,
England need to win at least two of the remaining three Tests, avoiding defeat in the other, if they are to retain the Ashes they have held since 2009.
The tourists recalled seam bowler Tim Bresnan at the expense of spinner Monty Panesar, while all-rounder Ben Stokes kept his place at number six.
Tall pace bowlers Steven Finn, Chris Tremlett and Boyd Rankin, all of whom have been out of form on the tour, missed out, but Saker said England may have made selection mistakes on a pitch that is likely to offer increasing pace and bounce.
England bowled too short - Smith
"We assess that all the time and try to make sure we get selection right," said Saker.
"Like everything, we make mistakes, like cricketers make mistakes.
"We could have made a mistake in this game but I'm sure if our bowlers bowled to their capabilities we wouldn't have got it wrong. We picked the side we thought would get 20 wickets and I still think we can."
Smith had scored only 60 runs in the series before the third Test at the Waca, but compiled his second Test century to remain unbeaten on 103 overnight.
The 24-year-old scored 81 of his runs on the leg side, including a hook shot off Stokes to go to three figures, and said that England bowled a poor length
"They might have bowled a little bit short in patches," said Smith.
"I think, when we come out and bowl, we're going to be a yard fuller - and we hope that will create chances for us."
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