The under-fire Toffees head coach said that his side dominated the contest for 80 minutes and defended well for the remainder of the game.
"Apart from the last 10 minutes we dominated the game. There was only going to be one winner. We didn't score the second goal and they put us under pressure in last five minutes and we defended well," he told Sky Sports News.
"We go into Huddersfield next week to see if we can carry on this run. We've moved up the league one place.
"We're on track and going in the right direction. Well done Theo Walcott - three goals now as well as his assists. It's a game-changing winner."
Walcott scored the only goal of the evening, firing Everton up to eighth in the table.