Staley fell when he tried to navigate past a puddle outside the coaches' basement offices.
The Eagles, who are looking for the city to move ahead with plans for a new stadium, reacted angrily.
"I'm big on everybody doing their job, whether it's coaches, myself," coach Andy Reid said. "I am very critical of myself. The coaches, the players, it's important that everybody does their job.
"Obviously, somebody didn't do their job in there and were very negligent. To be very honest with you, that bothers me. That upsets me."
The Eagles said they called the city Thursday evening about the leak. However, nothing was cleaned up until after Staley fell. Staley was taken for X-rays, which the Eagles said were negative.
"It was a problem," Reid said. "Honestly, it was a scary minute there. He took a big-time spill.
"There was a leak in a pipe upstairs from what I understand. I didn't go up there and check that pipe, but I do know that one of my coaches has water in his office and there's water outside that area there. I believe they were notified last night (Thursday) about it, and it didn't get done."
The spill coincided with NFL commissioner Paul Tagliabue's visit with Mayor John F. Street. The Eagles have proposed a plan to the city in which the Eagles would be responsible for much of the cost of a football stadium, but the two sides have not actively negotiated terms of a deal for the last several months.
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