The Clarets angered Leicester and the home crowd with their time wasting in Saturday's 2-2 draw.
Maxwel Cornet - who scored Burnley's second goal - was booked after coming back onto the pitch for treatment having injured his hamstring.
Kasper Schmeichel came 40 yards out of his goal to complain to referee Chris Kavanagh about Cornet but Brownhill remains unrepentant.
"I think it is part and parcel of football," said the midfielder.
"You go through every game and whoever is winning is not going to speed things up.
"It is all about seeing the game out and for us we were not going to just get the ball back in and boot it up the pitch straight away because they have some quality.
"We wanted to calm the game down and take it at our pace and I think if it was the other way round I think everyone would do the same.
"I don't think we did it too bad because the referee would have probably booked players or the goalkeeper. It happens in football and you do anything to get that win and for us it is quite desperate at the minute."
Burnley are still searching for their first Premier League win of the season after Jamie Vardy's 85th-minute equaliser.
Vardy's own goal - the first of his career - gave the Clarets the lead before the striker levelled in the first half.
Cornet's goal, on his full debut, put the visitors on the brink of their first win at Leicester since 2007 before Vardy's second and they remain 19th and face pointless Norwich at Turf Moor on Saturday.
Leicester sat 12th after the draw and defender Timothy Castagne felt they allowed Burnley to take a point.
He told the club's official site: "We can't give them easy chances and goals like that. We have to be tougher. The Premier League is not easy, but I think we're shooting ourselves in the foot in the last few weeks, so we have to get back to our form.
"It's definitely two points lost. We have the same ambitions as last year. We want the three points against every team and, especially at home, we have to do a lot better.
"We'll work on that. As I said, we need to find our form again, and then we'll maybe get some wins in a row and get going.
"We've seen glimpses, but it's not like last season. We have a lot of things to work on. We have to say, we created some chances, but it's difficult. I'm never satisfied and I think the whole team can't be satisfied with that."