The East London based outfit played in front of 54,000 fans and head coach Slaven Bilic revealed that he though West Ham deserved the victory.
Friday's draw will include sides dropping out of the UEFA Champions League qualifiers, with Shakhtar Donetsk, Fenerbahce and Anderlecht among them.
"Basically we have five games before the September worldwide break and this squad is not big enough".
"You go there and think it is fantastic to play, and teams are going to come here and think that so we are going to have to be on the ball for the whole season".
Bubbles bounced across the turf at the packed new stadium and suddenly, with 50,000 serenading the display it felt like home. It doesn't matter, we want to try.
The first leg will be played in Romania on August 18 before the reverse in London the following week.
Sofiane Feghouli made sure of the win late on against the Slovenian minnows with a goal of his own, meaning a first success in five European games for United who crashed out at this stage 12 months ago.
"It was hard psychologically for us but, for the stage we are at, we played really good".
Aaron Cresswell and Manuel Lanzini are definitely out through injury and rumour has it that Gokhan Tore was training separately yesterday and is likely to miss the game in order to ensure his fitness for the start of the season.
Italian giants Juventus will officially open the stadium on Sunday in a high-profile friendly against the new hosts and all of the fanfare is being saved for then.
It was only a matter of time before Bilic's men scored again and Kouyate struck on 25 minutes, following good work from Michail Antonio initially and then Carroll, who poked the ball through for the Senegalese midfielder to fire home.
"There's no point comparing it to Upton Park. We don't have a mountain to climb, but a job to do".
"We have to be positive and I'm totally positive, the players are not afraid of it, they like it".
Bilic did confirm striker Diafra Sakho's potential move to West Brom could be close to completion, as could the arrival of Sao Paulo forward Jonathan Calleri on a season-long loan.