The Millers manager was full of praise for opposite number John Ward, whose first nine games in charge of the home side had produced six wins and two draws.
But Evans rightly felt Rotherham shaded a tight Memorial Stadium contest after Kayode Odejayi and Lee Frecklington struck within the space of two minutes to put them in control with Joe Anyinsah replying for Rovers nine minutes from time.
"We feel that if we match the effort of opponents, we have the quality to beat them and that is what happened," said Evans.
"John Ward has done an unbelievable job in recent weeks and we knew if we let Rovers get ahead their confidence would be boosted further.
"But we defended well throughout and took our goals well. I thought we should have had a couple in the first half because the chances were there.
"Rovers scored a great goal, but apart from that our goalkeeper barely had a save to make. To be honest I thought they would cause us more problems than they did."