Ramsey will leave for Juventus in the summer, having agreed to join the Serie A giants on a free transfer when his Gunners contract expires.
The 28-year-old injured his hamstring during the second leg of Arsenal's Europa League quarter-final victory over Napoli and, while Emery's original estimate was that Ramsey could be back within two or three weeks, he will now miss the remainder of the season.
Emery's side take on Valencia in the first leg of their Europa League semi-final on Thursday night, having lost all three games without Ramsey since he was forced off in Naples.
But, even if Arsenal reach the final in Baku on May 29, Emery conceded the game would come too quickly for Ramsey to be involved.
Asked if there was any chance of Ramsey playing in the final, Emery replied: "At the moment we are only in the semi-final, and secondly the prognosis is not okay for this date.
"He is important for us. We cannot use him and the danger is always there for a forward player like that.
"We have players who can play (in that position), but he was in a good moment when he had this injury.
"For me it was a good experience to work with every player and with him especially, because he can transmit his energy and he showed me his heart is red with Arsenal.
"I wanted to enjoy with him. I said to him one month ago that I wanted to do something important in his last matches with us at the moment - maybe he can come back in the future. It will not be with him on the pitch but he is still with us."
Press Association Sport understands Arsenal are liaising with Juventus over his recovery and the Wales international is expected to be fit in time for start pre-season in Turin.
It is also understood that the club are planning to hold a guard of honour for Ramsey and retiring goalkeeper Petr Cech after Sunday's match against Brighton at the Emirates, their final Premier League home game of the season.
Koscielny will lead Arsenal out against Valencia almost a year to the day since he suffered a serious Achilles injury in last season's Europa League semi-final defeat at Atletico Madrid which saw him sidelined for seven months and miss France's World Cup win.
The 33-year-old has played alongside Ramsey since joining from Lorient in 2010 and, in a jibe at previous Arsenal players who have left the club during that time, the defender hailed Ramsey's attitude since his move to Juventus was announced.
"Of course he played so may years here, so important for the club and the players because every season we start the season and we have new players, and I think he gives a lot for the adaptation of the new players," he said.
"What I like about Aaron is that, we know he signs for Juventus, but he is still a professional and always fights for the club and for the team.
"Sometimes you have players who have stopped fighting for this team, but I think he has loved this club and that is why he stayed at 100 per cent for us. It shows a great mentality and character."
Mesut Ozil is in the squad for Thursday's clash with Valencia after missing the 3-0 weekend defeat at Leicester with a bruised foot, while Nacho Monreal also trained following a groin injury.
Meanwhile, Denis Suarez will return to parent club Barcelona after his unsuccessful loan move was cut short due to a groin injury.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies