The Millers lost to an 86th-minute goal in his first match in charge, at home to Reading.
But the 54-year-old, who was given a rousing reception by the New York Stadium crowd, saw enough in the 1-0 defeat to believe that he can pull off a rescue mission in the 32 remaining league matches.
“I felt the workrate, effort and commitment of the players was very good,” he said. “We went toe to toe with Reading. We had a good number of chances and were a threat from set-pieces, we couldn’t convert them.
“We are disappointed to lose the game but the players have to keep up that effort, workrate and attitude and not get too disappointed.”
Rotherham created the afternoon’s best chance, with Danny Ward being foiled by Ali Al-Habsi when he was clean through, before Paul McShane scored a close-range winner four minutes from time.
“There is a lot today we did well as a group,” Jackett added. “There is enough of the season to get things going.”
The Millers won one and drew three of their 13 second-tier matches under previous boss Alan Stubbs and are bottom of the table after seven straight league defeats.
But Jackett said: “Yes, I definitely feel I can keep them up.
“Taking six points out of 39 takes its toll on players. But they can’t be disappointed.”