The decision proved controversial to some but Poyet insists it made sense to the entire squad.
The Hammers were criticised by the FC Lusitans manager for lacking respect, as reported by Sky Sports, with new boss Slaven Bilic deciding to watch the first leg at Upton Park from the stands and allow his assistant to take charge instead.
It was clearly not something that had a negative effect upon his side as they qualified via comfortable 3-0 and 1-0 wins, and Poyet says the decision made sense to all the squad.
“I know Slaven Bilic was criticised for not being in the dugout against Lusitans,” he wrote on Kicca.
“Terry Westley, the U21 coach, took the game because he’s known all the players for a long time and that makes sense to me and to the rest of us.”
Bilic wants to get to know the players' games
The Croatian took charge at Upton Park last month, replacing former manager Sam Allardyce at the club after his contract came to an end.
He has been tasked with bringing a more attractive brand of football to the club, with former Newcastle boss Allardyce having been regularly criticised for not playing 'the West Ham way' during his tenure.
Before he can do that though, he will obviously have to set to work assessing the squad he already has and Poyet says the decision to allow Westley to take charge was simply an opportunity for Bilic’s to see everyone play in person.
“The manager still came in after the game and we also trained with him beforehand in Ireland,” he added. “He wants to get to know everyone and see how they play in person. The idea was always to let Terry take it from the start. Didn’t matter who it was against.”