Almirón suffered a hamstring injury after 64 minutes of United's 3-1 win against Southampton which ruled the Paraguayan international out for the remainder of the season.
Benítez revealed that Lascelles will also miss the away clash due to a week long illness sustained by the club captain but the Spaniard declared Issac Hayden and Fabian Schär fit to play against Albion, despite the pair both being withdrawn against the Saints after picking up worrying knocks.
Benítez said: “The bad news is that we have lost (Sean) Longstaff, (Florian) Lejeune and now Almirón (to injury). Miguel went to see a specialist in Spain and he has had his treatment. Everything is going according to plan and he's quite positive and keen to do everything right. He's a really good professional.
"We have also lost Lascelles because he has had a stomach illness all week. It is nothing too serious but he has not been training during the week with the team. However, I think Schär and Hayden will be available."
With Newcastle mathematically safe from relegation, the Magpies travel to the Amex Stadium against a Brighton side, managed by former United boss Chris Hughton, who remain in desperate need of points to secure Premier League survival.
The Seagulls have failed to score in their last six winless top flight contests while Newcastle - who currently bestow an identical record from last season - lie seven points adrift of tenth place as the Magpies go in search of securing a successive top-half finish.
Benítez added: “We know Brighton really well. It’s a difficult situation now for them - they have three fixtures which are quite difficult. The way I can expect they will approach the game is attacking and trying to score an early goal, putting our team under pressure and getting their fans behind their team.
"He (Chris Hughton) has done really well at Brighton. It is more difficult for him this year because the Premier League may be more difficult than the previous one. He has continue competing but it's not easy. If you win one game, you can go two or three positions higher in the table or you can lose confidence. They have a problem right now because they are not winning at the moment and not able to score goals and they could feel more depressed.
“It’s really good that Newcastle United will be there (in the Premier League next season). We knew from the start that it would be difficult and a very tough season but we did very well. It's a credit to this group of players - they were fighting for each other, fighting for the shirt, fighting for the fans and, in the end, we are where we are because we were consistent.
"We had the belief that we could do it and carry on. I was analysing the games with a lot of players individually and as a group and talking about how close we were in every game, such as Brighton, Tottenham and Chelsea, apart from a couple of games. We are happy for that and now we will try to go as high as possible in the table.
"You have to approach every game with the belief that you can get what you want. I think that has been a key part for these group of players, who were working hard for each other, the fans and the club. It doesn't matter what happens at the start of the season when you lose games. We saw consistency and a good mentality which has been the key for me."
