Key midfielder Jan Kirchhoff will require a scan to determine the extent of the hamstring strain suffered in the 1-1 draw with Montpellier HSC.
But there was more promising news on striker Jermain Defoe, who is said to be progressing "very well" after picking up a thigh strain in training earlier this week.
No date has yet been set for his return though and with the Premier League kicking off a week on Saturday, his absence for any length of time would be a major blow.
German midfielder Kirchhoff and Billy Jones both limped out of the action in the first half of last night's draw with Montpellier HSC at the Stade Jaques Forestier, the final match of the French tour.
"Jan went off with a little hamstring strain," Stockdale told the Echo.
"He will have a scan, which is standard, and we won’t know too much about that for a few days.
"We’re not too concerned about Billy’s hip, he really just came off as a precaution."
He added: "Jermain is progressing very well actually.
"I wouldn’t like to put a date on it, but we are confident that it is not half as bad as we originally thought."
Kirchhoff pulled up off the ball and after a few minutes of trying to play on, he signalled to the bench he couldn't continue and walked from the field.
Within five minutes, right-back Jones also limped off the pitch to be replaced by Seb Larsson as David Moyes was forced to make two changes to his team before the break.
Meanwhile, left-back Patrick van Aanholt wasn't risked after suffering tightness in his groin against Dijon FOC on Wednesday night.
The pair were joined in the stand at the ground in Aix-les-Bains by Jack Rodwell, who had strapping on his right calf.
When asked about van Aanholt, Stockdale added: "It was a decision we had to make and in the end we felt it just wasn’t worth the risk.
"Anyone who saw Patrick play last year will know that his fitness levels are fantastic.
"He did some light training Friday, and if it had been a competitive game rather than a friendly then he would have played.
"Jack picked up a little niggle in training on Friday, but that’s all it was.
"Touch wood, we haven’t picked up anything major in pre-season - not when you look at other clubs and see that they have players who are going to be out for months.
"We certainly haven’t got anything like that.
"I think our injury picture probably looks a bit worse than it actually is."