Roberto Martinez was delighted with the composure his side showed to overcome an in-form West Ham side.
An 81st-minute Romelu Lukaku strike proved decisive on an afternoon that could have been incredibly frustrating for Everton.
Instead, the manager was able to reflect on the patience and quality his side showed to secure three points.
He said: "It was exactly what we expected. West Ham are a team in form in terms of results, with four straight wins and a draw at Chelsea. They are very well organised and confident in their defensive duties.
"What pleased me more than anything is that we never got emotional or frustrated. We never left ourselves exposed or lost our concentration, which is easy against a side like West Ham that is very efficient in the final third. To restrict them to one shot on target is a magnificent achievement.
"What is important is that on a day like today, at home against a side like West Ham, when everyone expects you to win, it could have been all too easy to get emotional and frustrated after losing the way we did last week. It gave me incredible satisfaction to win the way we did and I think you will see this side at its strongest in the next 11 games.
"We're not looking at where we are going to finish - we are looking at how well we can finish. And then we will see where that leaves us."
"We want to win every game and, if we do that, who knows where we will finish. We've got five games away and six at home. This league has got many twists and turns until the last second.