The Clarets' victory, their fifth in six home games in the Premier League, came courtesy of a double from the 38-year-old Scot.
Alexander told the Lancashire Telegraph: "It was really important that we got back to winning ways it was disappointing last week to lose our home record.
"It was a massive game for us today and we're pleased to get the three points. You have to fight and scrap for everything you get in the Premier League and we did today and got the three points.
"We have just got the believe in ourselves and each other which the gaffer instils in us and hopefully that will be enough.
"I think we deserved the three points today, we played some cracking stuff at times.
"We just had to make sure we kept our concentration at the back."