West Ham boss Slaven Bilic was relieved after his side edged Birkirkara on penalties but insisted they have to learn from the experience.
The Hammers relinquished their first-leg advantage early on to Fabrizio Miccoli's strike for the Maltese side, before they went down to 10 men as James Tomkins saw red just before half time.
Bilic's charges held firm to deny Birkirkara, who also had a man sent off in extra time, and take it to penalties, which they won 5-3 to advance to the third round of Europa League qualifying.
"The most important thing is that we are through," he said on www.whufc.com.
"They started better and they were very aggressive. After they scored we took control of the game, but we didn't create chances, even though we we were around the box a lot and passing the ball.
"We lacked either the determination or quality to go into the box and create clear-cut chances."
Bilic was particularly frustrated with the red card, which was issued to Tomkins for retaliating after Nikola Vukanac pushed him in the back before a set piece.
"That's two rounds, two stupid red cards, first in Andorra and now here"
It was a second dismissal for the Hammers in as many rounds - after Diafra Sakho's red card against FC Lusitans - and Bilic wants his side to get more streetwise on the European stage.
"That's two rounds, two stupid red cards, first in Andorra and now here," he added.
"We didn't get used to playing in Europe in this kind of atmosphere. We have to adjust, because we cannot react like that to provocation.
"It will happen again, 100%. Both of them were a little bit hard for me but we gave them a chance to give us red card.
"After that, it was much harder for us. We were the better team at end of the game, but we didn't create a lot and we didn't penetrate enough."
The most pleasing aspect of the evening for the new Hammers boss was the penalties, though, after Mark Noble, Mauro Zarate, Aaron Cresswell, Joey O'Brien and Diego Poyet were all successful.
"When it came to the penalties, they are a lottery, but all five guys took them really, really good. I saw confidence in their eyes when I asked them who would take them," he said.
"More than five wanted to take them, we were confident and it happened and we are through."
