Solanke was substituted in the 40th minute with a muscular problem, while Simons was replaced in the 63rd minute after suffering a knee issue.
Despite the setbacks, the 82nd-minute winner from Joao Palhinha secured Tottenham’s first league victory in 16 matches at Molineux. Spurs remained 18th in the standings with 34 points from 34 games, two points from safety.
"Solanke has a muscular injury. I don't know what level of injury, and for Xavi it's a problem of the knee, and we're going to see in the next days, Monday or Tuesday," De Zerbi told reporters.
"For Solanke, it's not a big problem. I don't know how many games we lose him, but I would like to know the real situation of Xavi, because the knee is always different than the muscular injury."
Tottenham, who are facing the prospect of their first relegation from top-flight football since 1977, have four games remaining and next travel to Aston Villa on Sunday.