Rashford limped off after he was caught on the right ankle by a heavy challenge by Sergi Altimira, and Antony followed just 23 minutes after coming on as a second-half substitute.
Both players were able to sign autographs for fans afterwards as they left the Snapdragon Stadium walking relatively freely, and are being assessed to see if they can face Liverpool in Columbia, South Carolina on Sunday morning.
With Rasmus Hojlund out for six weeks and new £36.5m striker Joshua Zirkzee only just having started pre-season training at his new club, manager Erik ten Hag needs Rashford, in particular, to be fit for the start of the new season.
United face Manchester City in the Community Shield at Wembley on August 10 before kicking off their Premier League campaign against Fulham at Old Trafford six days later.
Antony, who came on a second half substitute, also saw his evening cut short against the LaLiga outfit
Ten Hag also has the option of playing a false nine after Jadon Sancho filled that role against Real Betis.
He added: ‘I think we have to assess next week where we are, they are in two very different situations. Jadon is in pre-season, he is in the tour, Joshua has played in the Euros, then had his break and now started training this week.
So next week we have to assess those and pick a team that is capable to win the game against Manchester City.’