Jefferies said: "After a disappointing first half we were more like ourselves after the break and we might have been two or three goals ahead after 10 minutes of the second half.
"The players never let their heads go down and it was a great goal that clinched the point for us. We showed a great deal of resilience throughout the match."
Jefferies had seven players unavailable for the Scottish Premier League match and fresh injuries to Grant Murray and Simon Ford will stretch the Rugby Park side's resources to the limits.
The manager was delighted with the performance of former Celtic and Leicester player Momo Sylla who, due to the developing injury situation, played in three different positions during the match.
And Jefferies is now hoping his side can climb back into the top six by taking heart from the overdue victory.
Kilmarnock also face Falkirk in the CIS Insurance Cup in just over a week's time.
"The win over United should boost the players' confidence," said Jefferies. "We have had a tough run of fixtures recently.
"It was a great win for us."