The result extends Liverpool's winning streak to five games and will undoubtedly fill Steve Cooper's side full of confidence ahead of the Reds' important clash with Tottenham Hotspur next weekend.
Trickett-Smith - who lead the line in the absence of Jerome Sinclair and Jack Dunn - continued Liverpool's recent clinical streak in front of goal when he fired in their first opportunity of the match.
That was enough to separate the two sides as the valiant Reds' defence remained sturdy throughout the match.
West Ham looked to cause an immediate shock inside the first two minutes when full-back Kyle Kanoyle raced down the right flank to grasp the first chance.
Fortunately for the Reds, the youngster met a cross with a tame effort that enabled goalkeeper Ryan Crump to smother the shot with ease.
Despite a bright start from the Hammers, Liverpool dealt the visitors a crushing blow with their opening attack of the game.
The skillful Alex O'Hanlon charged towards the back-peddling Reece Burke before deftly chipping the ball past the defender and towards the back post, allowing Trickett-Smith to calmly side-foot a volley past Sam Baxter.
This was the catalyst for Liverpool to stamp authority on proceedings as they began to dominate possession and create further opportunities.
Just after the half-hour mark, goalscorer Trickett-Smith provided fellow attacker Kristoffer Peterson an inviting chance to extend the Reds' lead.
The Swede rose to power a header towards goal but was foiled by Baxter who reacted well to prevent him from close range.
With little more than five minutes remaining in the first period, Peterson proved to be a nuisance for the Hammers' backline as he tested the visitors' goalkeeper yet again.
The youngster raced forward to meet an incisive pass from midfield, as he surged towards goal he was tripped in the box by full-back Lewis Paige. Despite slightly losing his balance, the winger admirably remained on his feet as he tried to slot the ball into the net, but Baxter anticipated the danger well and rushed off his line to block the attempt.
Not content with a mere one-goal margin, the Reds pressed in search of a more comfortable scoreline swiftly after the restart.
O'Hanlon was eager to cause more havoc in the Hammers' area when he drilled a dangerous cross into the six-yard box. His efforts to find a Liverpool player were in vain as West Ham quickly cleared amid pressure from several Reds lurking in the area.
Harry Wilson - who replaced the energetic Peterson at half-time - was presented with an excellent opportunity by the influential Jordan Rossiter 11 minutes into the second half.
The Liverpool captain effortlessly played a defence-splitting pass towards the onrushing winger who hesitated before striking the ball straight at Baxter.
As the Reds constantly pushed in search of a greater goal tally, West Ham countered with just less than 20 minutes remaining in the game.
Intricate passing play between the Hammers' midfield allowed substitute Thomas Gogo to slide the ball across to Kieran Sadlier, who was in acres of space.
The youngster failed to take advantage of a rare chance as he slammed the ball straight at Crump.
Following this, Cooper's charges cruised to a deserved victory as they restricted the frustrated visitors to no more opportunities, rounding off a fine showing.