Barkley suffered medial ligament damage in training on Friday and was left out as Everton were held to a 2-2 draw at newly promoted Leicester City in their Premier League season opener at the King Power Stadium on Saturday.
The 20-year-old has undergone scans, but Martinez stated that they did not reveal the extent of the problem, leaving the Spaniard unsure of how long Barkley will be on the sidelines.
"Ross Barkley is a phenomenal footballer and we will miss him. He was sharp in pre-season and came back with a different approach and mindset," Martinez said.
"It was very unfortunate to lose him to an innocuous challenge in training. Now he's going to be out for a long, long time.
"The squad should be able to cope but it is disappointing. We have to cope with our frustration and make sure he can cope with what's left of the season.
"He had a scan but it was difficult to determine. We don't know how long he will be. It was the medial ligament in his knee and we still don't know how bad it is.
"It is a partial tear of the ligament. It can be anything between seven weeks and four or five months. We need to be a bit cautious."
The injury means that Barkley is set to miss England's opening 2016 UEFA European Championship qualifier in Switzerland next month and will likely see him unavailable for the games with San Marino and Estonia in October.
But Martinez has faith that Barkley will be able to bounce back from the blow.
"Ross is a very mature boy, he was very disappointed as he was looking forward to the start of the season and put a lot of work in," he added.
"He knows how to cope and we will be with him and make sure he is not suffering too much. We will make sure he comes back strong.
"Playing in a World Cup is a highlight but he had a good season last year. It was a moment of form he has found in himself.
"He had a very good break and couldn't wait to come back. But to get to the final session before the season is frustrating."
