Matchwinner Welbeck said: "The lads gave 100%, it's difficult obviously with the first leg. Very difficult to take that defeat. We paid the price with the first leg. We knew we could get a result in front of the fans tonight but it was too much to do.
"We've got a lot of very good players that are out (injured) as well. With the squad, we have to be proud of ourselves and we did the best that we can do.
"Nice to get the goal. Last week I got some good headers and the keeper made some good saves. It was nice to get that goal but tonight it's not enough."
On getting back into Europe, he added: "We want to keep improving and progressing as a team and as a club. There's a great culture at the club."
"We're going to do our best to get back to playing in these competitions.
"Brighton (being in the Europa League) is historical, first time in Europe, bringing European football to Brighton was massive in itself but there are some steps we need to take to keep bring European football to Brighton."