Sylla has not started a Premier League game for Villa since December and his last appearance came as a first-half substitute in the 4-1 home defeat by Stoke City over a month ago.
He expressed his frustration at the situation last week and stated that he would be keen to return to French football on loan next season.
Lambert has suggested he would have preferred Sylla not to voice his displeasure, but has challenged the 23-year-old to break into his starting line-up
"I understand people's frustration at not playing," said the Villa boss in the Birmingham Mail.
"I think that's normal at any football club. You wouldn't expect people to want to sit there and not play.
"I think that's normal so you're glad in that respect. Should he have spoken out? Probably not, but that comes with experience and I'm glad he's feeling disappointed at not playing.
"The three lads in the middle of the pitch have been playing really well for us so Yak's got to do his utmost to get into the side.
"He's got a chance here. He's got to try and force his way into the side."