A double from Lewis Grabban sealed the points, the second coming right at the end but missed chances nearly cost the Millers as Morecambe came back twice to draw level.
But Evans was pleased overall with the 3-2 win and told Radio Sheffield: ""We're highly delighted, the disappointing thing was at half time to go in at 1-1.
"I said to the boys that I was disappointed with the quality in the final third and we had to work a little bit harder, we've done that right from the whistle after the break.
"We did it the second half with ten men but we missed a big chance at 2-1 to go 3-1 up - if that had gone in it would have definitely would have been a four or five scoreline."
Ryan Cresswell was booked twice meaning he was dismissed for conceding a penalty before Grabban's late heroics, and Evans had no complaints at the decision.
"You didn't really notice the referee today, he;s a good ref and I think the decision was correct, Ryan would have missed the one game with 2 yellows or a red either way."