Partington was replaced by Donal McDermott following a heavy challenge from Adam Chapman towards the end of the second half.
The 22-year-old was selected alongside Harry Arter in the centre of midfield for the season opener at the Kassam Stadium.
Manager Paul Groves is currently without strikers Frank Demouge, Josh McQuoid and Charlie Sheringham but was reluctant to use the injury problems as an excuse for his side’s League Cup exit.
“Fletch trained for one day (before the Oxford game) and we’ve got three other strikers out, and that would have an impact on anybody. That’s something we will have to deal with at different times this season, so I won’t make any excuses,” he said.
“I thought at that end of the pitch we lacked a cutting edge or that final pass, and at the start of the season sometimes that work takes a little bit of time to get right.”