Roberto Martinez's Toffees came from a goal down to cruise past the Swiss club at Goodison Park in the Round of 32 second leg, recording a 7-2 aggregate, which has them as the only UK team still alive in Europe's second tier club competition.
After the match, Martinez spoke of the way his side went about their task after taking a 4-1 lead into the return bout and admitted there is some buzz around the club ahead of Friday's Round of 16 draw.
"I'm very pleased. We had a very good lead and sometimes that can affect how you want to perform," he told the club's official website.
"To be the last British team in the Europa League is satisfying. Scoring seven goals in the tie was great to see.
"There will be excitement tomorrow at the training ground surrounding the draw, but we want to take every game as it comes."
Romelu Lukaku, who scored a hat-trick last week, netted twice while Kevin Mirallas was also on the scoresheet as the Toffees made light work of the Bern outfit on a night where Merseyside rivals Liverpool, Premier League adversaries Tottenham and Scotland's Celtic all crashed out.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball