Malky Mackay said: "I'm satisfied with the performance and the result. We were playing a difficult customer because of the way Doncaster play.
"I've known how they play for a long time and Sean is the longest serving manager in the league.
"They are always a threat going forward with nimble, nifty players who create chances and play off lines. They always threaten your goal so I'm delighted with the clean sheet.
"But we started on fire and we came close to scoring twice in the first minute.
"We did the same in the first minute of the second half as well so I was delighted with the way we set to our task in both halves.
"It took time but I thought our fitness, particularly in the second half, showed. There was a frustration with a few of our final passes and we gave away some decent possession.
"But, overall, we lifted the tempo, showed we had learnt from our mistakes in the first half and did more than enough to earn the points - which you have to do to get anything in this division - to win the game."
After a first-half stalemate, Gerrard broke the deadlock with a glancing header from Peter Whittingham's teasing cross in the 52nd minute.
Then Earnshaw was back on the scoresheet just days missing an open goal for Wales against England last week.
But Mackay insisted he had no doubts over his forward, who slotted home from close range with 15 minutes remaining as well as hitting a post as Cardiff maintained their promotion charge.
Mackay said: "Good players and good guys at their sport have an inner self-belief that they keep doing the right thing. Eventually you succeed.
"I had no doubts about Robert Earnshaw scoring goals at this level and for Wales."
Cardiff rarely looked in danger against the rock-bottom visitors, who had not recorded a win since March 1.
Doncaster manager Sean O'Driscoll said: "We didn't play well enough to win the game.
"When you are bottom of the league with just one point then every game becomes massive. The more you go without winning games then the harder it becomes.
"What can go wrong is going wrong and for the first time this season we were tentative. We may need to make some harsh decisions about the players. We lacked courage to play."