Despite losing Marten de Roon to injury and seeing Gaston Ramirez sent off as they fell nine points from safety, Agnew is adamant they have not given up.
Their performance at the Vitality Stadium, in which they were uncharacteristically poor in defence, left them in 19th, and their five remaining fixtures are against Sunderland, Manchester City, Chelsea, Southampton and Liverpool.
However Agnew, who has overseen four defeats and two draws since his appointment, said: "It's very emotional. There's lots of angry players, lots of emotional players, as there is staff. We'll all be in tomorrow morning and address the situation.
"We have to be realistic. It's a huge, huge challenge, but all we can do is dust ourselves down and get ready for Sunderland (on Wednesday). Every game we need a win. We remain as positive as we can be.
"In many ways we lost the game in the first 10 minutes. That's not like us. It was really, really poor defending. Playing short passes on the edge of our area is another reason we concede. It's just naive defending.
"It is (unusual). That's what disappoints me; it's not like us. We made mistakes, got punished, and it made it a very, very difficult afternoon.
"I couldn't see (Ramirez's first booking) from where I was, the initial one, but if you have a yellow card you have to be very, very careful for the rest of the game.
"Playing with 10 men in the Premier League, against a good team at home who score lots of goals, gave us a very testing afternoon.
"It's (also) difficult yet to say the extent of the damage (to De Roon's ankle)."
Referencing the shock death on Friday of club favourite Ugo Ehiogu, he added: "What a sad, sad day. Our condolences go to the family; the supporters were amazing again."