The American was out of sorts for much of a match which lasted two hours 29 minutes. He was also fined $1,566 (£1,000) for his behaviour.
Enqvist went on to beat Michael Chang in the final, 0-6, 6-4, 6-0.
In the first set tie-break, Agassi smacked a ball from the baseline to the other side of the court, sending a linesperson jumping out of the way and knocking down the radar gun.
After losing the tie-break, Agassi threw his racket from his side of the court to a table behind the umpire's chair, knocking over drinks and flowers. "I just don't think umpires should get involved in the game because they are not part of it," Agassi said. "They overrule on a 118-mile an hour serve and they don't overrule at 15-30 in the third set. To me it's very disruptive."
In the other semi-final Chang, the defending champion, beat Dutchman Paul Haarhuis, conqueror of Pete Sampras, 6-2, 6-0, in just 51 minutes.