West Ham United drew 1-1 with Manchester United last week.
West Ham drew 0-0 with United at Old Trafford last weekend, and they could have won the contest if they were slightly more ruthless.
The Hammers were without a number of key players due to injury, but the draw extended their impressive sequence of results away from home.
And Bilic said to the London Evening Standard: "Considering our ever-lengthening injury list at the moment, I could not speak more highly of the players at Old Trafford last weekend.
"The team had a spirit, a togetherness, a determination which showed itself in what was a superb performance — one which could easily have brought us victory.
"With so many offensive players missing it is that kind of spirit which we must replicate in every match, right through what will be a hectic Christmas period.
"I told them that we have to repeat this in every game now — but even more because that is the only way we can compensate for the loss of so many of our players."
The Hammers have been one of the Premier League’s most dangerous teams on their travels this season.
Bilic has guided them into seventh place in the top-flight table, but their form has dipped more recently.
West Ham have failed to win any of their last five matches, and an injury which Winston Reid picked up in midweek has stretched their squad even further.
The Hammers’ next match comes against Stoke City at Upton Park, where they will be determined to get back to winning ways, to ensure that they maintain their place in the upper echelons of the Premier League standings.