A first-half effort from French attacker Cyril Thereau was enough to secure victory for Udinese in Thursday's clash at the Stadio Olimpico.
The defeat leaves Lazio with just three points from their first four Serie A games, however, former Germany international and World Cup winner Klose has confidence in the Italian capital club's ability to recover.
"We created so many chances without being able to find the goal," Klose told Sky Sport Italia.
"We lacked luck. We played very well, but we just could not score the all-important goal.
"This Lazio side is the strongest since I arrived at the club, we have been working very well in training and I am sure we'll come back stronger after this game."
Meanwhile, Udinese coach Andrea Stramaccioni was quick to praise his players following a success that made it three league wins in four for the former Inter boss' side.
"Beating Lazio is an important step for this team," Stramaccioni said.
"What impressed me tonight was our mentality.
"Today [Thursday] the team has grown a lot, particularly in the second half when we defended well without looking like conceding."
