Butchart's time of 13 minutes 13.30 seconds ensured a second Olympic qualifying standard.
He must finish in the top two at the British Championships in Birmingham next month to make the Games in Rio.
"Getting the second Olympic qualifier was the priority," Butchart told Scottish Athletics.
"Now I can go to Birmingham with the pressure off in terms of chasing the time."
Butchart beat Muir's record, which had stood for 36 years, by over four seconds.
"I didn't think about (the record) in California a couple of weeks ago when I went close but my coach and I did say last week that if the race in Holland was as fast as we thought it might be, then there may well be a chance to PB and take the record," added Butchart.
"Others can still spoil the party for me, I guess, but I definitely think that for the likes of myself, we've take away one of the barriers.
"The race was fast and I knew with about 800m to go that I'd get the national record. It wasn't the worst feeling in the world, I must admit!"
Butchart was troubled on the last lap of his race by loose laces in his spikes, eventually kicking one shoe off and completing his record-breaking run.
"Before you ask, I had them tied properly - nice and tight - at the start," he said.
"But it was wet and the rain seemed to loosen them as the race went on. It wasn't quite like running in flip-flops but it was getting to be a problem.
"With 400m to go I looked down and the right shoe was completely loose and my heel was in danger of coming free. I just had to kick that one off and away and get on with it. I was thinking, this isn't the best time for this to be happening.
"But you just get on with things, don't you? Lots of things can happen in athletics and you have to try and stay focused."
Earlier on Sunday, Eilish McColgan ran 15.16.51 in her 5000m race to finish sixth and earn a second Olympic standard. Josephine Moultrie was in the same race and clocked 16.05 for 11th place.
Steph Twell raced in the 1500m and recorded 4.10.90 for seventh place. There were sixth places for Allan Smith and Guy Learmonth in the high jump (2.15m) and 800m (1.47.23).
Meanwhile, in Rabat, Lynsey Sharp went to the top of the British rankings with her first 800m outdoor run of the season, clocking 1.59.51 to finish fifth.
Despite running the final lap in one shoe, Andrew Butchart broke Nat Muir's 5000m Scottish national record at the FBK Games in Holland.