Although they still sit fifth following Monday’s disappointing 20-13 loss at Wakefield Trinity, they could be usurped out of the top-six by seventh-placed Hull in Newcastle on Saturday.
With just two regular rounds then remaining, Agar knows they would face a fight to regain their place in the end-of-season reckoning.
Hull, though, are in a similar position after a dreadful defeat at Salford Red Devils left them with just one win in their last seven outings.
“With this game in particular, our sentiments are the same,” conceded Agar.
“It’s must-win for a number of reasons for both of us.
“We don’t like to term games as must-win but given our respective league positions, because it’s so close to the end of the year and also the fact it’s not two points because of the win percentage...
“It’s almost more than that in the context of the season because we play each other.”
Leeds beat FC 22-12 at MKM Stadium recently but Hull prospered 18-12 at Emerald Headingley in May.
“We’re both on the back of disappointing performances,” added Agar.
“We’d shown some good form until Monday and then had a really disappointing performance. We need to fix that up.
“We’ve played Hull twice already, both have been fair contests and both teams had a right go at each other.
“The last one was a really tight contest just a few weeks ago and it was decided late on. It all makes this a really interesting fixture for both.”
Meanwhile, Agar “feels” for Callum McLelland with news the luckless half-back is expected to miss the rest of the season.
The Scotland international, 21, came off with a knee injury at Wakefield.
After a frustrating time sidelined, he had been enjoying his chance with fellow Leeds pivots such as England scrum-half Luke Gale and the versatile Liam Sutcliffe already ruled out for the rest of the campaign.
However, Agar said: “Callum got taken off with a pretty serious injury. We’re awaiting the scans of that but it’s likely we’ll miss him for the rest of the year.
“We really don’t know much more. He wasn’t feeling great this morning and the patella tendon is the initial thought in terms of the injury.
“The exact damage is unknown at this point.”
McLelland, out of contract at the end of the season and linked with a return to Castleford Tigers in 2022, has simply not been able to get going this year.
Agar said: “I feel for the kid. He had to be patient waiting for an opportunity and he got some last year, and he would have had more opportunities this season.
“He’s had a pre-season and then a whole season that’s been punctuated with numerous injuries. He’s been stood down on Covid and now he’s had a cruel way to finish his season as we’re coming into the business end. We really needed him in the halves but he’ll bounce back. He’s still young enough and good enough. He’s got a long and fruitful career in front of him.”