The Kiwi prop missed last Friday’s Betfred Super League defeat by Wigan Warriors after being sent-off during the Challenge Cup tie against St Helens.
The RFL’s disciplinary committee banned Tetevano after upholding the match review panel’s grade D charge.
He had admitted the striking offence, but challenged the grading.
Leeds could have attempted to get the length of the suspension reduced, but Agar revealed: “We are not going to appeal.”
He said: “We were disappointed with the grading and the outcome of the tribunal, but such is the way the procedure goes, we thought it would be a futile experience to go and challenge it again.
“We’re not even sure we had grounds for appeal, given the way the wording is for how you can appeal.
“We were very pessimistic given the outcome and the way the first hearing went that we would have any grounds or any chance of an appeal.
“We have had to accept it, but we are disappointed with the severity and what we thought was the harshness of it.”
Agar stressed he had no complaints about a ban, but felt four games was “excessive” for the tackle concerned.
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