"We knew coming here we would have to be very good in our structure and defensively. But it was more courage and mentality today," said Monk.

"We let ourselves down last week, that was a big thing for us and we talked about that side of it. Today we put that right.

"I know it was only three games – before that we's were six unbeaten and doing very well in the league. Three defeats and everyone thinks the world's ending.

"We were just disappointed with ourselves and wanted to put that right.

"(It was) a long trip for our fans so (we had) even more determination to make sure they went home with something to cheer about and I think they'll be very proud of that result."

Wednesday's previous win over top-flight opposition in this tournament came courtesy of goals from Chris Waddle and Mark Bright at Wembley in the 1993 semi-final against city rivals Sheffield United.

Around 2,200 travelling Owls supporters celebrated wildly when winger Reach ended that run by smashing home his second goal of the season with 25 minutes remaining after being teed up from a free-kick.

The visitors comfortably hung on against last season's semi-finalists, although their joy was tempered by 12-goal top scorer Steven Fletcher being carried off on a stretcher with a knee injury.

Monk must wait to discover the extent of the problem but revealed Scotland international Fletcher had undergone an X-ray and not suffered a broken bone.

Wednesday had made six changes for the third-round tie, including handing a senior debut to 19-year-old right-back Osaze Urhoghide, while Albion opted for seven alterations.

The Seagulls were jeered off by sections of the home support at full-time after producing a below-par performance and failing to threaten an equaliser.

Brighton boss Graham Potter admitted his side were poor but refused to blame individual players for the loss.

"We didn't play well. We lacked a bit of fluidity, a bit of cohesion," he said.

"It was a flat performance, we couldn't really get going.

"We had some opportunities, first half, but it probably wasn't a great game of football and in the end Sheffield Wednesday overall deserved to go through. Good luck to them.

"We huffed and puffed but without the usual quality we like to have.

"I don't like to throw anybody under the bus, that's not what I'm about. Today, as a collective we weren't good enough."

Veteran striker Glenn Murray was left out of Brighton's squad amid reports of a January departure.

Potter insisted Murray's absence was purely fitness related.

"He picked up a knock in training. We had a few that were bumps and bruises and fatigue and it was just one of those," added Potter.