Premier League outfit Spurs suffered a 2-0 loss to the Italian club at the Stadio Artemio Franchi in Florence in the second leg of the round-of-32 tie on Thursday.
Mario Gomez put Fiorentina in the lead in the 54th minute, and Chelsea-owned winger Mohamed Salah secured the win with the second goal on 71 minutes.
The defeat in Italy saw Spurs lose the tie 3-1 on aggregate and fail to progress to the last 16 of the Europa League.
Tottenham academy coach Allen has now highlighted two reasons why Spurs failed to defeat Fiorentina on Thursday.
"It was a first-goal game tonight,” the 43-year-old told BBC Radio London. “Spurs showed enough in the first 45 minutes but Roberto Soldado's miss ultimately cost them.
"These games are often determined by a tactical change and Vincenzo Montella got it right.”
Spain international striker Roberto Soldado missed a great chance in the first half when he had only Fiorentina goalkeeper Neto to beat.
The former Valencia star decided to pass the ball to Nacer Chadli, but Neto intervened and the chance went abegging.
Fiorentina scored twice in the second half to deservedly win the tie as coach Vincenzo Montella continued to impress, but one wonders what would have happened had Soldado scored from that glorious chance.
Winning the competition would have given the North London outfit a chance to feature in next season’s Champions League campaign.
Now, Tottenham need to finish in the top four of the Premier League to stand a chance of playing Champions League football in 2015-16.
Spurs will return to action on Sunday when they take on Chelsea in the final of the League Cup at London’s Wembley Stadium.
It will be interesting to see if and how Tottenham recover for Sunday’s big game.