Parker suffered the sprain late in the first half of the Spurs' 93-89 win over the Dallas Mavericks on Monday to knot their first-round series 2-2 with a pivotal Game 5 coming Wednesday at AT&T Center.
"We'll see how he is tomorrow," Popovich said.
Parker played through the injury in the second half, finishing with 10 points on 5-for-14 shooting, three assists and four turnovers. He is averaging 15.5 points and 4.5 assists for the series.
San Antonio did not practice on Tuesday, using a day to regroup after seeing a 20-point second-half lead slip away against the eighth-seeded Mavericks before holding on to win.
Popovich said that the fact that the Spurs, the No. 1 overall seed in the playoffs, had to recapture the lead after falling behind with 4:50 to go in the fourth shouldn't make any more of a difference on his team's psyche than if they ended up blowing Dallas out.
"I guess theoretically that's a notion that you could entertain, but in the playoffs I don't think teams are ever too satisfied with wins or ever too depressed with losses," Popovich said. "You just don't have time for it and it doesn't do you any good. You just move on and sometimes handling a win is tougher than handling a loss. Coming back from a loss is relatively natural. Your body reacts. But human beings have a tendency to relax when things are going well. So that's what we want to fight."
The Spurs bench, which had been underwhelming through the first three games of the series with 35.7 points per game (well below its 45.1 points per game average during the regular season), scored 50 points in Game 4.
While Manu Ginobili led the Spurs' reserves with 23 points, it was Boris Diaw (17 points) and Patty Mills (10 points) who provided unexpected lifts. Diaw's 3-pointer with 32.0 seconds left in the fourth broke a tie game and put San Antonio up to stay.
"It was a big shot," Popovich said when asked to compared Diaw's make to some of Robert Horry's old exploits. "Rob's hit a few bigger."
Mills had just 12 points, three rebounds, three assists and two steals through the first three games of the series combined before going for 10 points, three rebounds, two assists and two steals in Game 4 alone.
"He led our activity," Popovich said of Mills, who could see extended minutes if Parker is hobbled by his ankle Wednesday. "That hell-bent for leather sort of activity is important in a playoff game. Sometimes people refer to it as 50-50 balls and that kind of thing. It's got to be there because there are opportunities for guys to involve themselves in plays and I thought he was very active."
The Spurs hope to keep up that activity, particularly on the defensive end. San Antonio has held Mavs star Dirk Nowitzki to just 16.0 points on 38.5 percent shooting through the first four games.
"As I've said many times, you're not going to stop Dirk," Popovich said. "He's one of the greatest players we've ever had in this league. To think you're going to stop him is foolish, but the goal is to try to make Dirk work as hard as possible and I think that Tiago (Splitter) and Boris are doing that."
After tying up the series on the road, Popovich was asked if he has any feel for how the Spurs will respond now that they're back at home for Game 5.
"I stopped trying to figure out how the game would start a long time ago," Popovich said. "I didn't think we'd start in a hole (Monday), didn't expect to blow the other team out. You just play the game and just keep on pushing."