Like his opposite number on Saturday, Millwall's Joe Edwards, he has been parachuted into a Championship relegation battle in his first management job on the back of his coaching calibre but the fragile confidence of the players the German has inherited was starkly obvious when they were thrown to the Lions.
The one mitigating factor in losing three of Rohl's first four matches in charge without scoring was that they had all come away from home. At Hillsborough they had been bursting with positivity and quality against Rotherham United. That 2-0 win looks even more damning on the Millers after this 4-0 battering.
One goal, too easily headed in at a 31st-minute corner by Murray Wallace was all it took to take the wind out of the sails of the team bottom of the Championship.
At least Rohl did not sit on his hands, making a triple halftime substitution after George Savile's sweet strike had doubled the damage, but it made little difference.
Although Josh Windass forced a block and two good saves after coming on, his team were already 3-0 down by then, a calamitous Cameron Dawson error allowing former Rotherham defender Wes Harding an easy third goal in four games.
When confidence is already low, having a goalkeeper who adds to the jitters is the last thing you want.
One the fourth went in, courtesy of another former Rotherham defender, Brooke Norton-Cuffy, the Kop practically emptied. They had lost confidence in their team too, and you could hardly blame them.
It was a world away from the joyous celebrations at the end of the last game many of them attended.
The game turned on an Anthony Musaba miss in the 29th minute.
The match had been even until then, with neither side registering a shot on target. George Byers struck a volley into a defender, Harding cut out a dangerous Callum Paterson ball and Di'Shon Bernard came over at the other end to put an excellent penalty-area tackle in on Tom Bradshaw
Musaba ought to have forced the first save when Barry Bannan drove through midfield and slipped him in but after taking a decent touch, the youngster's shot was wild, even allowing for a slight bobble.
The Owls paid a high price for it minutes later when Dominic Iorfa was rooted to the spot as Wallace jumped above him to head in a George Honeyman corner.
At that point, the home team's confidence evaporated.
Former Middlesbrough midfielder Saville added a wonderful second goal in the 43rd minute, hitting the bouncing ball sweetly with the outside of his boot when it was pulled back to him from the right.
Before the half-time changes could take effect Millwall had scored a third which owed too much to Dawson, sliding out at Bradshaw but spilling the ball to Harding, who finished calmly.
Leading the line in the second half, Windass hit a shot into Jake Cooper and had two well kept out by Bartosz Bialkowski.
The introduction of Bailey Cadamareri – son of former Huddersfield, Leeds Unbited, Sheffield United and Bradford City forward Danny – to play off him was warmly greeted but a deflection denied him a goal on his Football League debut and John Buckley thumped a header wide at stoppage-time corner.
But all Wednesday got from the latter stages was a Paterson booking which will rule him out of the trip to Birmingham City after the international break.
Millwall added a fourth in the 72nd minute, Norton-Cuffy nutmegging Musaba and gliding through with ease.
"We want five!" chanted away fans who have not been used to seeing wins of any size lately.
Wednesday look utterly demoralised, the task ahead gargantuan.
Sheffield Wednesday: Dawson; Iorfa, Diaby, Bernard; Paterson, Bannan, Byers (Hendrick HT), Johnson (James 75); Musaba (Buckley HT), Gassama (WIndass HT); Fletcher (Cadamarteri HT).
Unused substitutes: Palmer, Vaulks, Ihiekwe, Vasqueuz.
Millwall: Bialkowski; Norton-Cuffy (Leonard 84), Harding, Cooper, M Wallace; Honeyman (Esse 69), Saville (Mitchell 75), De Norre, Longman (Emakhu 75); Flemming; Bradshaw (Nisbet 84).
Unused substitutes: McNamara, Hutchinson, Campbell, Trueman.
Referee: G Ward (Surrey).