Milan coach Sinisa Mihajlovic was thrilled with his team’s performance in their 3-1 win at Lazio late Sunday and felt they fully de-served the three points.

The Rossoneri clinched a third straight win in Serie A for the first time this season and climbed into sixth in the standings.

The visitors also brought an end to Lazio’s perfect run at home.

Milan, who had not beaten Lazio at the Stadio Olimpico since 2009, were 3-0 up with 11 minutes remaining thanks to goals from Andrea Bertolacci, Philippe Mexes and Carlos Bacca.

“That was an important win,” Mihajlovic told reporters.

“We had to win to give continuity to our recent performances and we did so.

“We were worthy winners against Lazio. My players showed a great team spirit and I can only be delighted.”

The victory saw Milan reduce the gap to joint Serie A leaders Fiorentina and Inter to five points.

“We need to take it one game at a time,” Mihajlovic said.

“The important thing is that we have moved up in the standings and we look more solid. We create a lot of opportunities and give away few chances.”

The Rossoneri looked to be heading for a second straight clean sheet but conceded a goal six minutes from time.

“It’s a pity that we gave away a goal that we could have avoided. But it was nevertheless a good performance,” Mihajlovic said.

Lazio had won all of their previous eight games in Rome but came unstuck on Sunday.

“My players lacked rhythm and Milan closed our spaces,” Lazio coach Stefano Pioli said.

“We conceded goals at crucial times of the match.”

The loss, Lazio’s second consecutive in Serie A following a 2-1 defeat at Atalanta last time out, dropped the side to seventh place ahead of next Sunday’s showdown at arch-rivals Roma.

“Now we must think about the derby which is very important for us,” Pioli said.

“Lazio will need a great performance to get a good result in order to lift our morale. We have lost two straight games and now we need to get back on track.”

Lazio, unbeaten in the Europa League, visit Rosenborg on Thursday before taking on Roma.

“We will try to prepare in the best possible way for Thursday’s game at Rosenborg,” Pioli said.

“The Europa League is an important competition for us and we know that victory in Norway would see us through to the next round.

“Then, we will focus on next Sunday’s derby.”