On a dry and rutted surface in Ukraine, Spurs missed the chance to take a lead back to White Hart Lane next week when Roberto Soldado inexplicably missed the target from four yards after being set up by Paulinho after 55 minutes.
The visitors were made to pay for that profligacy when Jan Vertonghen brought down Brazilian forward Matheus in the box in the 81st minute and Yevhen Konoplyanka - a target of Liverpool during the January transfer window - stepped up to tuck the resulting penalty in off the post.
The winger's spot-kick sparked a frantic ending to the match that saw both sides hit the woodwork, but Sherwood remained upbeat despite his side's first defeat in Europe this season.
"Credit to Dnipro, they played well," he told reporters. "We know we can do better and the positive thing is we're still in the tie.
"I can't fault the endeavour and application from the lads. We just needed a little more quality at certain times.
"We now bring them back to the Lane next Thursday and hopefully we'll stay in the competition."