In a written statement issued Saturday, Eichorst said he and the university "very much look forward to our upcoming bowl game and Coach Pelini continuing to lead our program in the future."
Pelini was in the media spotlight Saturday after the Cornhuskers fell to Iowa at home 38-17 Friday.
Pelini was penalized for unsportsmanlike conduct for a sideline tirade directed at officials.
He told reporters after the lackluster game if Nebraska wanted to fire him, they should go ahead.
"I believe in what I've done," the prickly Pelini said. "I don't apologize for what I've done. I don't apologize to you. I don't apologize to anybody."
Pelini came under fire in September when a 2-year-old audio tape of him blasting the fan base was released.
Nebraska is 8-4 this season and will likely receive a bowl bid. However, the season included sloppy losses to UCLA, Minnesota and Michigan State that knocked them back in the BCS race.
Eichorst had declined to comment on Pelini much of the season as a matter of policy, but said Saturday he felt the need to say something "given the volume of unfounded speculation and conjecture about our head football coach."