Both players suffered ligament damage in last Saturday's 2-2 draw at Sunderland, but the club had previously been reluctant to put a timescale on their recovery.
However, speaking ahead of Southampton's FA Cup fourth-round clash against Yeovil Town on Saturday, Perez confirmed the duo could face two months on the sidelines.
"They are serious injuries," he said. "We initially expected Gaston to be out longer than Dejan, but they’ll be out for the same time."
The Spaniard also hinted manager Mauricio Pochettino could rotate his squad for the visit of Yeovil, with Arsenal set to visit St Mary's in the Premier League on Tuesday.
"This is a good game for us. It’ll be an opportunity for some players," he continued. "We have two games in a short period, so we have to choose the right squad for the game.
"We have to pick the team bearing in mind that we have another game on Tuesday.
"This week, three or four players from the development squad have trained with us."
But Perez insisted the approach did not detract from their desire to go as far as possible in the competition, adding: "We take every single opponent seriously. We’re expecting a difficult game.
"It doesn’t matter that Yeovil are near the bottom of the Championship. They will play without pressure.
"Our aim is to get into the next round. The FA Cup is important for the fans and the culture of this country."
