The 39-year-old was slow to get down to the first of Bilal El Khannouss’ two goals and made a poor attempt to claw away a low drive from Jamie Leweling.

The Dane has come under criticism for his performances since returning from a shoulder injury last season and scoring an own goal in Celtic’s Scottish Cup final defeat by Aberdeen.

Benjamin Nygren briefly had Celtic level in the first half but the Bundesliga side were comfortable winners in the first leg of the knockout round play-offs and Tiago Tomas rounded off a poor night for Celtic with a stoppage-time effort.

Celtic beat Stuttgart on their way to the 2003 UEFA Cup final under current boss Martin O’Neill but the 73-year-old’s focus will surely now be on the domestic campaign, even ahead of next week’s second leg in Germany.

That game comes at the start of a four-match run of away games in 10 days, which also sees Celtic travel to Ibrox twice either side of a trip to Aberdeen.

The first leg witnessed a false start as dozens of mini orange and yellow balls were thrown on to the pitch in the opening seconds as Celtic fans continued their campaign of protests against the performance of the board and an ongoing ban of the Green Brigade ultras group.

Celtic squandered some early chances to deliver set-pieces of quality and one led to a counter-attack which the hosts looked to have dealt with. But a series of sloppy passes and clearances – the final one from Schmeichel – ultimately allowed El Khannouss to beat the goalkeeper with a shot that went just past his left foot in the 15th minute.

Some high pressing paid off for the hosts six minutes later. Nygren intercepted a pass from Stuttgart captain Atakan Karazor, rounded the goalkeeper and slotted home his 16th goal of the season.

However, the Swede was at fault as Stuttgart regained the lead in the 28th minute. The midfielder failed to track El Khannouss in the box and the Morocco international guided home a free header from six yards following a looping deflected cross.

The German side had another couple of decent chances before the interval and went 3-1 up in the 57th minute. Leweling drove the ball from 22 yards almost directly at Schmeichel, whose decision to scoop the ball away backfired as he only helped it into the net.

The former Leicester player was on the end of loud boos from his own fans when he next touched the ball and he was soon beaten again by Ermedin Demirovic. This time VAR came to his rescue as the goal was ruled offside.

The boos continued every time Schmeichel got the ball in the subsequent five minutes.

Nygren soon forced an excellent save with a low drive but Celtic struggled to create clear chances and only came close again when Marcelo Saracchi shot just over from very long range.

A Schmeichel save from a low drive from Tomas drew sarcastic cheers from home fans, most of whom left after the same player netted from close range three minutes into stoppage-time.