Everett was placed on the 15-day disabled list after the game and was replaced on the roster by Eric Bruntlett, who was recalled from Triple-A Round Rock.
Lee said he made a last-second call for the ball, but it was too late.
"I called it a little late," Lee said. "We looked at each other and said, 'We've got to go for it.' I kind of called it but he was coming already. We thought the same way. We were looking at each other and said, 'I've got to go for it.' That's why we got caught in the middle.
"I feel bad. You don't want to see a teammate go down like that. It's just frustrating."
Immediately after the collision, Everett lay flat on his stomach, unable to move. He was eventually carted off by assistant athletic trainer Rex Jones.
Everett said later he initially went numb after the collision, just before he was overcome by the pain.
"It definitely wasn't pretty," he said. "I knew something wasn't right. I was hoping it wasn't my knee or ankle. It was an eerie feeling. I don't know how to explain it. My whole body went numb after the pain went through. As soon as it hit me, it was excruciating. I went numb for a second, then it started hurting."
Everett placed no blame on Lee for the mishap.
"I don't think it was anybody's fault," he said. "It just happened. One out of 1,000, it's not going to happen. It's just unfortunate, obviously.
"He said something real late and I didn't have time to get out of the way. I just didn't want the ball to drop. I didn't hear him until it was too late."
Everett has no idea how long it will take for him to return to the field, but he was encouraged that the injury was to a "non-weight bearing bone."
"There's nothing wrong with the ankle and knee so this is the best thing that could possibly happen," he said. "As soon as I can start to put some weight on my leg, I'll be able to begin to walk."
Manager Phil Garner said Bruntlett will share the playing time at short with Mark Loretta.
Bruntlett, 29, was hitting .279 (63-for-226) with 10 doubles, four triples, one homer and 21 RBIs over 60 games for the Express at the time of his recall. He was recently named offensive player of the month for May after hitting .362 with nine RBIs.
Bruntlett has played in 91 games over portions of four seasons with the Astros, compiling an average of .251 (84-for-334). In 2006, he hit .277, logging 33 hits in 119 at-bats.
While Everett is arguably in a class of his own when it comes to defense, Bruntlett could be categorized as somewhat of a defensive whiz as well. He can play seven positions, including all three in the outfield. During his time with Round Rock, he played three games at first, four at second, 14 at short and 43 in the outfield.
"In my career, Eric Bruntlett has made a few spectacular plays when I've been pitching," closer Brad Lidge said. "He is definitely a defensive specialist, but he can also provide really good at-bats, too.
"He's definitely a guy that can help us out. If there's anyone that can help us out there and do things close to Adam, he's one of those guys that can. He's a very, very solid player. We need that right now."