The Blades' second home league defeat of the season has left them six points adrift of the automatic promotion places behind Brentford and the top two, Tranmere and Doncaster.
Defender Higginbotham, making his home debut after signing recently on loan until the end of the season from Stoke, told the Blades' official website: "It's very frustrating and disappointing, both in terms of the performance and ultimately the result.
"Yeovil deserve some credit, but we are angry at our own display, which led to the defeat.
"We know what we're capable of and I've seen it already. We have the ability to bounce back from this result and I'm sure we will.
"Everyone will take this kind of result to heart, but we'll come back stronger."
Danny Wilson's side, who have taken only one point from their last three league matches, will bid to bounce back on Saturday at Notts County, who have lost their last three home games.