Kai Havertz finished a superb pass from Gabriel Martinelli for Arsenal's 1-0 quarterfinal first-leg win after the pair came on in the second-half.
Borges said afterwards: "It’s frustrating. It’s only natural to feel a bit frustrated after the great game we played here against a top-class side.
"If you look at the 92 minutes, we had three or four clear-cut chances, whereas they had none apart from the disallowed goal. We just needed to be a bit sharper in front of goal. That’s football; let’s keep our heads up and believe that it’s possible."
Sporting now go to London needing to overhaul a 1-0 deficit.
Borges also stated: "I believe we need to be mature and intelligent in our approach to turning the result around, bearing in mind that we’re playing against a top-class side that can make the difference in the tiniest of spaces, as was the case with today’s goal.
"I’m now firmly convinced that we’ll be competitive in London and that we’ll see this tie through to the end."