A late penalty from Liverpool target Yevhen Konoplyanka settled the first leg of this round-of-32 tie in favour of the Ukrainian side, although both teams were guilty of missing several chances - with Tottenham stiker Roberto Soldado the main culprit for the visitors.
The Spain striker turned a glorious 55th-minute chance over the bar from close range with Spurs in the ascendancy.
Sherwood, whose side were blocked by UEFA from training on the pitch on Wednesday, questioned the state of the surface after tasting defeat in his first European outing as a manager.
"He would expect to score," Sherwood said of Soldado's chance.
"I haven't seen it again but I'm not sure he will be too complimentary about the pitch.
"I am not using it as an excuse, not for the chance, as both teams played on it but I am sure that it must have played some part in Robbie missing that one.
"The pitch was a disgrace, it is no excuse as both teams had to play on it but it is possibly the worst pitch I have experienced in a long time."
Konoplyanka's penalty came 10 minutes from time after Jan Vertonghen had brought down Brazilian striker Matheus inside the box, but Sherwood is certain his side will play better in the return leg at White Hart Lane next week.
"We could have played better," he conceded.
"I didn't think we were very poor but the disappointment that we never scored and we had some good opportunities to do that.
"We will score at the Lane, guaranteed, but it depends how many we will have to score."
Former Tottenham boss Juande Ramos is in charge at Dnipro and he revealed he sent his side out to accrue a first-leg advantage, rather than look to draw the game with the hope of springing a surprise in seven days.
"Our target was to score as much as possible, a draw was not for us," he said.
"Luckily we were just able to score the goal which gives us some advantage but we are pretty aware of the fact that London we will have 90 difficult and serious minutes. We will do our best and try to win in London."
Ramos' evening could have been even better had Tottenham goalkeeper Brad Friedel not made a number of good saves, including keeping out a deflected Konoplyanka free-kick late on.
Roman Zozulya hit a post with a header in injury time but Ramos is happy to be heading to England with a lead of any margin.
"I must say that the match today showed that both teams would do their best to win," he said.
"We were pretty close to scoring the second goal which would be great help for us in London but still I have nothing but thanks to the players for what they did.
"Two-nil would have been really great for us. But we have 1-0 and we are looking forward to the second leg and will do our best there."