Evans set up Wayne Rooney to fire home what turned out to be the winner against the Cottagers on 42 minutes.
But despite dominating possession for the most part, the Reds were unable to add to their tally thanks to some heroic defending from the visitors and some excellent saves from goalkeeper Mark Schwarzer.
"It's a great result for us but we're a bit disappointed with the performance," he told MUTV and Sky Sports.
"It would have been nice to get more goals but looking back on the game I think we just have to be delighted with the three points, especially as the performance we put in probably wasn't up to our usual standard.
"Things were a bit nervy towards the end - we gave away a few free-kicks and invited a bit of pressure onto ourselves.
"The fans were getting a bit restless and you could feel it in the atmosphere. We maybe needed a bit of composure and to take the easy pass rather than the hard one. But we defended well in the situations we found ourselves in and managed to grind out a victory which puts us top of the league again."
The Reds survived a late penalty shout when Michael Carrick appeared to clip the heels of Danny Murphy in the area, but referee Michael Oliver was unmoved.
"You have a quick look towards the referee, but he's waved it away. I haven't seen it back again but he could have given the penalty," admitted Evans.