Romelu Lukaku denied the Hammers a point with a goal nine minutes from time at Goodison Park and ended their fine run of winning form in the Premier League.
But Taylor says they have to continue looking up at the teams ahead of them in the table, rather than down at the relegation places as it was just over a month ago.
He said: "We conceded a lot of pressure and space, in the main we defended well. We just didn't do enough, particularly in front of goal. Everton are hard to come to, and had we got a point we would have deserved it.
"You have to take the positives. We would have loved to get a win with the run we've been on.
"We are tough to break down but when we have possession we need to use it more in final third. If chances keep coming for them they'll take one - that's the Premier League, the most unforgiving in the world.
"Losing hurts, we haven't had that feeling for a few weeks. It's international week and some of us will have a bit of time of so we have more time to prepare for Stoke and we want to go on another run like the one we just had.
"Everything is a work in progress, there aren't many teams in the position they want to be but we're looking better than we were a few weeks back. There's the games to go, we're in the top half, we want to cement our position there."
Defender Guy Demel added: "Of course we are disappointed after defending so well, a draw would have been fair.
"Next week we have a game at home and we have to stay happy and work hard.
"Of course there is still work to be done, every Premier League game is hard. No-one gives you points for free, that's why everyone wants to be in the Premier League.
"We knew when our heads were down, we could get ourselves out of the situation - we did that and we have to make sure we stay there."