With the club comfortable in sixth place in the Premier League, Bilic was able to play a strong side at Anfield to face Jurgen Klopp's kids.
But they failed to take advantage and will now welcome the Reds for a replay in East London next week.
Aston Villa have been improving in the league of late and are clinging on to an outside hope they might pull off a miraculous escape from relegation.
But if the recent erratic form of Dimitri Payet is anything to go by, they could be in trouble.
Patchy form is bad news for Villa and Spurs
The French star has been one of the players of the season so far and is already a hero to Hammers fans.
However, his form since his return from a two-month injury lay-off has been patchy. He was unbelievable in a 3-1 away win at Bournemouth, scoring a sublime free-kick and setting up a tap-in for Enner Valencia with some audacious skill.
But in the next game at Newcastle United, Payet was anonymous and hardly got a kick as the Hammers slipped to a 2-1 defeat.
When Manchester City came to town for last week's thrilling 2-2 draw Payet was again the best player on the pitch.
His vision, skill and touches were a joy to watch and it left fans and pundits salivating over his quality.
But at Liverpool in the cup he was once again very quiet and didn't look as sharp as usual.
Entitled to a bad game
The former Marseille man is of course entitled to the odd bad game and he wasn't the only West Ham player to underperform at Anfield in what was a glorious chance to do the treble over a much weakened home team.
It will be a worry for Villa and Payet's compatriot Remy Garde, though, given how good he has been after a poor performance in recent weeks.
With West Ham facing the prospect of closing the gap on bitter rivals Tottenham Hotspur in fourth place to just three points with a win over the bottom club, no extra motivation is needed.