The dual-code England international quit this week at the age of just 31 and only two months after returning to the sport on a two-year deal.
Half-back Eastmond played just two games but then realised his “passion to influence the game is no longer on the field” and he walked away from his contract.
Leeds were already in the market for another half-back/full-back for 2022 after Australian No6 Robert Lui - currently injured - confirmed he will retire at the end of the season.
Agar said: “This has forced it even more.
“It (recruiting) was something we were looking at.
“Jack Walker is down on a long-term injury, Robert Lui’s retiring and we’ve been playing Liam Sutcliffe in the halves.
“I don't think there’s any need immediately to get in the market.
"I think now, given what’s happened with Kyle, it’s really important for us that we don’t have another short-term move.
“Obviously, Kyle was never meant to be short-term but we don’t want to get there and end up with a player that's not going to be with us for too long.”
Agar, whose side host Hull FC on Sunday night, added: “Rob Lui’s fitness is hopefully around the corner which will help us for the rest of this season.
“But moving down the track we are going to need to recruit another half-back or spine player moving forward.
“Don’t ask me who at this moment of time. Like everybody else at this time of the year, we are talking to agents and looking for availability to see what’s a good fit for us.
“We need to make sure that after what’s happened with Kyle it’s a fit that will be for the next 18 months or two to three years.”
The Leeds chief praised the honesty of ex-St Helens star Eastmond who had battled to regain his fitness after more than a year out of action and on his return to rugby league a decade after initially moving to union.
“It was a really brave decision,” said Agar.
“We knew there was some risk and were really prepared to support him all the way through it.
“When we signed him, we were three or four weeks away from the first game and we thought he’d be fit for that.
“The basic struggle was getting to the right levels of conditioning for him.
“For every two steps forward, he took three steps back. Not from a rugby point of view but a physical perspective whether that be a sore hamstring or whatever, it impacted his ability to get on the training field and do what we needed to do.
“There was a realisation it was going to be a longer road back than what we probably anticipated and the honesty part from Kyle was that the fire wasn’t burning as strong as it needed to.
“He was very, very honest. I don’t think there’d be too many players who’d say I can’t be the player I know I can be and the one you need me to be so I’m not going to try and manufacture that.
“His honesty in the situation was quite remarkable really.
“It’s not ideal but nothing ventured, nothing gained and it wasn’t to be.”
Leeds picked up only their second win of the season when they beat Wakefield Trinity 15-13 on Friday.
They have ex-England scrum-half Richie Myler returning from a two-game ban against Hull on Sunday but Agar intimated at his press conference today that he would come in at full-back for youngster Jack Broadbent with Sutcliffe likely to stay at No6.