Brentford are into the quarter-finals of the Carabao Cup for the third time in five seasons and, as Thomas Frank led his team on a victory lap after beating Sheffield Wednesday on penalties, the thought occurred that the Dane will not spend too long dwelling on missing out on the Manchester United job.

There was a satisfied smile on Frank’s face, although he knew it had not been an entirely comfortable evening for his team. Brentford made heavy weather of it after an early goal from Kevin Schade, their focus and intensity fading after half-time, and they could have paid for their failure to kill off their Championship opponents.

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Wednesday, four points off a playoff spot and four above the bottom three, were there for the taking because of Danny Röhl’s decision to make nine changes before hosting Watford on Saturday. They were desperate during the first half, defending badly and playing without any cohesion, but they fought hard to recover and earned their reward. There were wild celebrations when Djeidi Gassama fired in the equaliser in the 57th minute.

It became a struggle for Brentford, clarity eluding them during normal time, their rhythm never returning. But the shootout was a different story. Wednesday’s 19-year-old goalkeeper, Pierce Charles, did not get close to nerveless spot-kicks from Bryan Mbeumo, Keane Lewis-Potter, Mikkel Damsgaard, Yoane Wissa and Vitaly Janelt. “Five very good penalties,” Frank said. “One very good save.”

Liam Palmer was the fall guy for Wednesday, the pressure on him when he stepped up to take their fifth kick. He had to score to force sudden death but Mark Flekken dived to his right to keep out a soft effort from the substitute. “It was tough,” Röhl said. “We had to make changes. We play on Saturday and then Tuesday again. But it was outstanding from my team. The message at half-time was we had to be more connected. We showed character to stay in the game.”

James Bree struck a late winner as Premier League strugglers Southampton survived a major scare by scraping into the Carabao Cup quarter-finals with a thrilling 3-2 victory over Championship side Stoke.

Goals from the Potters pair of Ashley Phillips and Tom Cannon threatened to force a penalty shootout after Saints blew a two-goal lead following Taylor Harwood-Bellis's header and Adam Armstrong's spot-kick. But defender Bree prevented a new low in a miserable season so far for the top-flight's bottom club by rifling home from range in the 88th minute at a sparsely populated St Mary's.

Southampton were fortunate to reach that stage still level as only a goalline clearance from Yukinari Sugawara stopped the Stoke substitute Million Manhoef completing the turnaround minutes earlier.

Brentford were dominant for much of the first half and they soon breached Wednesday’s unconvincing offside trap, the opening goal arriving when Lewis-Potter lifted a pass over the top for Schade to streak away from Gabriel Otegbayo and tap into an empty net after his initial effort was saved by Charles.

The tone had been set, the visitors struggling to prise the ball away from Mathias Jensen in midfield. Frank called him Brentford’s quarterback. Jensen resisted the press and kept looking for opportunities to spring Lewis-Potter and Bryan Mbeumo clear on the flanks. Lewis-Potter was tough to pin down and he had chances to double Brentford’s lead. He shanked one effort high and wide, then drew an acrobatic save from Charles after fastening on to an inswinging cross from Mbeumo.

Wednesday offered little beyond a dangerous run from Anthony Musaba. Dominic Iorfa summed up their growing frustration when he booted the ball into the stands after being played into trouble by a poor pass. It was not the greatest spectacle.

The crowd stirred when Mbeumo produced a lovely piece of skill and cut inside two defenders, only to shoot straight at Charles. Fábio Carvalho’s footwork often caught the eye but his decision-making was not good enough.

An air of complacency fell over Brentford, and they were punished after giving away possession in midfield. Gassama strode forward and when nobody challenged the winger he cracked a stunning low shot past Flekken from 25 yards. Now a proper game broke out. Wednesday threatened again, Ike Ugbo stinging Flekken’s palms. Brentford responded through Mbeumo, Charles beating his powerful drive away. Ugbo then shot wide from a tight angle.

It took until the 82nd minute for Brentford to come alive again, Wissa turning and feeding Schade, whose shot was turned behind by Charles. Penalties beckoned. Flekken came out on top and Frank could look forward to another cup run. He insisted that the links with United had made no impact on his focus before this game. He said the speculation was “nice for the ego”, but he has Brentford ninth in the Premier League and would love to keep this cup run going. Silverware, Frank said, is a realistic target if the quarter-final draw is kind. “I think we have a good chance.”