The New Zealand international has been out with a knee injury since the 2-2 draw away at relegation threatened Sunderland at the start of October – missing the last three games.
He returned against the Toffees and performed solidly, even though Romelu Lukaku scored once again against the Hammers, his seventh goal in seven against the east Londoners.
Reid said: “It can get better with my fitness because I have been out for a while and it has been annoying. I will get better as the season progresses.
“We were going so well for the team that I could take a bit more time to recover and make sure the injury didn’t come back. Hopefully that will be the case. I have been working really hard in the gym with the physios to make sure that I am ready to come back in.”
With the festive fixtures in sight, the upcoming international break is a chance for many of the players to improve fitness levels before facing London rivals Tottenham Hotspur away on November 22.
Two of those players are midfield star Dimitri Payet and striker Enner Valencia who both suffered worrying injuries against Roberto Martinez’s men.
Reid said: “It is different when you have been out for a while and try to come back in. But I thought in general the team played pretty well, you can see we are progressing in the way the manager wants us to play and everyone is learning and improving every day, that is the main thing. We have made a really good start to the season and we need to push on and keep going.”