After Tuesday's 5-3 home win over Barnsley, Millen was again full of praise for his players, as he had been after Saturday's 2-2 draw with leaders Newcastle.
"We lost Lewin Nyatanga with an injury in the warm-up and had three players struggling with knocks at half-time so it was a tremendous effort by the lads," said Millen.
"We again looked too open defensively and that may be something we have to put up with until the end of the season.
"But our two strikers, Nicky Maynard and Danny Haynes, worked their socks off to score two goals each and we always looked a threat going forward.
"We have another very important match at Peterborough on Saturday and if we can win that as well it may give the club more time to consider who will be the next manager.
"I am not thinking beyond that game and have not yet spoken to the chairman about my own future."
Barnsley boss Mark Robins preferred to praise City rather than slam his team's defensive deficiencies.
"They went into the game on the back of a great performance against Newcastle and played extremely well again," said Robins.
"I'm just disappointed we couldn't hang in there after going 2-1 up. We couldn't handle their pace up front and conceded some poor goals from our point of view.
"But it was a cracking open game between two sides who wanted to attack and we kept going to the very end. There was no faulting the effort of the players and if we continue to attack like that we will pick up better results."
Maynard was City's hero, scoring twice to take his tally for the season to 16 and being heavily involved in two of the other goals.
Haynes headed the home side in front from Marvin Elliott's early cross, but Barnsley were level within seconds as Hugo Colace volleyed home.
Daniel Bogdanovic shot his 14th goal of the season from Bobby Hassell's 25th-minute free-kick to give Barnsley the lead, but two minutes before the break Maynard nodded home after good work by former Barnsley winger Jemal Campbell-Ryce.
Maynard netted with another header on 55 minutes and then set up Haynes to make it 4-2 eight minutes later.
Paul Hartley fired City's fifth from the penalty spot after a foul by Ryan Shotton on Maynard before substitute Andy Gray headed a Barnsley consolation.
Campbell-Ryce only played because Nyatanga had felt his Achilles tendon prior to kick-off.