Boss Brendan Rodgers targeted a group win after Leicester registered their biggest European victory.
Kelechi Iheanacho's double gave the Foxes control of Europa League Group G as they breezed past Braga 4-0.
Dennis Praet and James Maddison also struck in the second half as the Foxes set a new European record, surpassing their 3-0 Champions League win over Club Brugge in 2016 and a 4-1 victory over Glenavon in 1961.
Leicester are top of the group, three points ahead of Braga, with Rodgers having been able to rest eight-goal top scorer Jamie Vardy.
Rodgers said: "Our objective is to win the group. We want to qualify but that's a few weeks away.
"We won against a good side, we played very well and when that next game comes we'll look at it from there.
"There were areas at half time we needed to adjust. They are a good side and gave us some problems, in the first half our midfield shape wasn't quite right.
"We scored four very good goals and maybe could have had one or two more."
Maddison impressed after being left out of the England squad for their games against the Republic of Ireland, Belgium and Iceland and revealed his disappointment.
"I want to be in the England squad, that's what I dreamed of as a little boy," he told BT Sport.
"I've had a taste and I want more. I'm back fit now and I'm firing, getting the minutes in the legs. I had a long injury last season and a couple of knocks this year, so I haven't had a consecutive run of games.
"I can't control whether I'm in the England squad, I don't pick the team, but I can only concentrate on Leicester."
Iheanacho opened the scoring after 20 minutes when he latched on to Maddison's pass, left David Carmo and – when the ball came back off Matheus – tapped in.
Goalkeeper Matheus denied Maddison in first-half injury time, but he was powerless to stop Iheanacho's second, the striker firing in from 25 yards thanks to a big deflection off Bruno Viana.
Abel Ruiz wasted Braga's only chance get themselves back into the game before Praet made it 3-0, tapping in Iheanacho's cross with 23 minutes left.
Maddison scored his second European goal when he wriggled past two tired challenges and netted from six yards, with Ayoze Perez close to a fifth when his deflected header hit the post.
Braga, who had won their last six games in all competitions, were brushed aside and boss Carlos Carvalhal knew where they went wrong.
"We competed in the first half and we are coming from a sequence of a game every three days and we have a very small squad," said the former Swansea and Sheffield Wednesday manager.
"The first half was even and their goal was unfortunate, we went in at half-time wanting to turn it around.
"But conceding a goal two minutes into the second half was a huge blow, we lost our organisation, opened up and that gave them the chance to exploit our team and we were tired."
