The Biancoceleste had gone into the match at the Stadio Olimpico on the back of two straight league losses and riding a six-match winless run in Serie A.
"Against Livorno I saw a determined team," Tare said to Corriere dello Sport.
"It was a huge relief because we need to win this game, more so, considering the difficult time we have gone through.
"The important thing is that the team has found calmness after the win.
"Now we must give continuity to this performance."
Lazio are eighth in the standings and end the year at Hellas Verona on Sunday.