The Hammers, meanwhile, also conceded twice in their most recent friendly, but David Moyes's men notched up six goals of their own during a resounding win over Celtic.
If Wednesday night's friendly was anything to go by, Brentford will make a fine addition to the Premier League, as the Bees came from behind on two occasions to hold Manchester United to a four-goal stalemate at the Theatre of Dreams.
Anthony Elanga and Andreas Pereira propelled United into the ascendancy twice, but Brentford's never-say-die attitude shone through as Shandon Baptiste and Bryan Mbeumo made the net ripple at Old Trafford in a highly entertaining spectacle.
Brentford were unable to post a fifth consecutive win of pre-season following triumphs over Wimbledon, Boreham Wood, Cambridge United and Watford, but Frank's side are building a healthy dose of momentum before they take on Arsenal in their first-ever Premier League match.
Southend United and Valencia lie in wait for the Bees before they mark their return to the top flight later in August, and Frank's side will undoubtedly relish the opportunity to test their strength against another club of European calibre this weekend.
A new manager has not brought new hope to Celtic just yet, and West Ham took full advantage of the Bhoys' misfortunes by marching to a 6-2 drubbing of the Scottish giants in front of an 18,500-strong Celtic Park crowd.
Ange Postecoglou's men may have been more concerned about their impending Champions League battle with Midtjylland - which ultimately ended in misery - and West Ham needed no second invitation to strike through Michail Antonio (2), Mark Noble, Said Benrahma, Jarrod Bowen and Armstrong Oko-Flex.
Callum McGregor and Ryan Christie found the back of the net for Celtic, but there was simply no stopping the rampageous Moyes machine as West Ham secured their third successive win of the pre-season period following victories over Northampton Town and Reading.
The Hammers are yet to take to the field at the London Stadium during pre-season, but they have strolled to victories away from their headquarters almost effortlessly - despite the return of home crowds - and free-scoring Serie A side Atalanta will pay a visit to Stratford for a tantalising final exhibition match.
A relatively friendly opening game to the Premier League season sees West Ham travel to Newcastle United on August 15, and while Hammers supporters will expect another strong season domestically, Moyes' side may already have one eye on their upcoming Europa League nights.
Once again, Brentford ought to field a near full-strength XI capable of going toe-to-toe with Premier League opposition, although new arrival Kristoffer Ajer was nowhere to be seen at Old Trafford.
Saman Ghoddos did not take part either, but Frank Onyeka did get some minutes as a substitute against the Red Devils, while Vitaly Janelt has taken no time at all to recover from a minor injury sustained earlier in pre-season.
Mbeumo could find himself alongside star striker Ivan Toney for this weekend's battle, while former Chelsea starlet Myles Peart-Harris will be optimistic about his chances of earning more minutes following a 15-minute Old Trafford cameo.
Meanwhile, West Ham also did not hesitate to name a heavily experienced lineup against Celtic, with the likes of Antonio, Noble and Bowen all starting and getting their names on the scoresheet.
Angelo Ogbonna suffered a minor injury scare against Celtic, but Noble has issued a positive update on his condition as he looks ahead to the opening day of the league season.
Head To Head
West Ham and Brentford have locked horns 48 times previously, with the Hammers boasting 22 wins compared to their opponents' 15.
However, given the Bees' lengthy absence from top-flight football, it has been 28 years since the two clubs last did battle competitively, during which West Ham claimed a 4-0 win in the 1992-93 Division One season.
We say: Brentford 2-3 West Ham United
Both Brentford and West Ham have demonstrated an affinity for goalscoring in pre-season, and this game ought to be another entertaining spectacle with plenty of experienced names on show.
The confidence in the two camps will be sky-high given their exhibition form so far, but we expect West Ham's superior first-team quality to shine through during a slim success.