The Germany international opened the scoring in the opening 45 minutes, before Mario Gomez, Muller a second time and Arjen Robben helped the Bavarians to a comfortable home win after the break, much to the delight of the 23-year-old.
"It feels great. We put in an outstanding performance. The way in which we beat them was superb – we gave everything. Everyone battled and ran their hearts out," the attacker was quoted as saying on the official UEFA website. "It's no secret that we have a lot of quality going forward. We've had some big wins recently, but to beat them like this in a game of this magnitude is just brilliant."
Muller then went on to admit that things are looking good for Bayern after the first leg, but stressed that the club is not there just yet.
"Everyone knows how strong Barcelona are at home, but we're in a great position and if I know this team, we'll be doing everything we can to progress," he went on. "Nothing has been decided yet, but things could certainly be worse."
The Germany international was about to be replaced just seconds before he made it 4-0 as he had picked up a knock and was understandably very pleased to double his personal tally before going off.
"I signaled to the bench that I'd picked up a knock before my second goal and was suffering from a bit of cramp, so I was preparing to come off, but we were still in possession so I had to keep going. Then I scored, which was obviously fantastic."
The second leg at Camp Nou takes place on May 1.