Robert Snodgrass' second-half goal saw off Spurs and edged City four points clear of the relegation zone.
But Liverpool's 4-3 Anfield victory over Swansea leaves Tottenham six points behind the Reds in fifth place.
Sherwood admitted Spurs now face a battle to overhaul their Merseyside rivals for a fourth-place finish to secure Champions League football next season.
Admitting the gap between Spurs and Liverpool is now considerable, the White Hart Lane boss said: "It looks big, it's a real blow to us but we've got to bounce back.
"We've got the second leg of the Europa League match and then we've got Cardiff at home.
"We need characters in the dressing room to be able to do that.
"We can't use Thursday's game at Dnipro as an excuse, especially as we were stronger in the second half.
"We created a few chances after going behind, but we just couldn't take them.
"It's the first major setback I've had as manager, and now the players must respond."
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