Seamus Coleman believes the Boxing Day postponement against Birmingham impacted on Everton at Upton Park.
Burst pipes at Goodison Park meant the clash had to be called off - just when the Toffees were on a high after beating Manchester City.
The postponement also meant David Moyes' side travelled to face West Ham on Tuesday having not played for more than a week.
Their opponents got a game in on Boxing Day - the morale-boosting 3-1 win at Fulham - and Coleman believes the Hammers benefited from this.
He told the club's official website: "There are two sides to it (the postponement) but I think it was (a hindrance).
"We were all ready to go and only found out late on so it was frustrating. It would have been nice to get a result on Boxing Day going into this game but it wasn't meant to be.
"It could have been a chance to get three points in front of the home fans, so it was frustrating.
"You could tell West Ham benefited from beating Fulham, and they had confidence."
Coleman netted his third goal of the season at Upton Park, with Hammers keeper Rob Green then denying Marouane Fellaini's close-range header with a sharp reflex save late on.
While Coleman wanted a win to push the Toffees up the table, he believes four points from their last two games - both away - is not a bad return.
He added: "We badly wanted all three points, and their goalkeeper getting man of the match shows that we probably should have.
"We were on top a lot in the game, but then we produced a few sloppy passes at times that let them come back on the break. We were unlucky to concede that goal, and it was disappointing.
"I scored but the team is more important to me and I'd rather have the points. It's a consolation to get a goal though.
"It's very frustrating, because you need to get a goal in the periods when you are on top. Their keeper made a great save from Felli and you wonder when you're going to get another chance as clear as that.
"We need to start taking the three points. After Manchester City we were all full of confidence.
"But if you look at it in a different way, four points from two games isn't really that bad.
"It was a frustrated dressing room though, and we need to start turning those draws into wins."