Hart received lengthy treatment at the time but continued and went on to earn the man-of-the-match award after a number of fine saves frustrated battling Palace in the second half.
It was a display that fully justified his recent recall to the side after a spell out but by full time the wound had swollen considerably.
But the 26-year-old has recovered well since and is not in any danger of missing City's next Barclays Premier League outing.
Pellegrini said: "Joe Hart has a cut beneath his eye but nothing important. It is not dangerous and he can play without any risk."
On the issue of Hart's form, after he was dropped in November and replaced by Costel Pantilimon for seven Premier League games, Pellegrini is convinced it is returning.
He said: "I hope, of course - everyone knows why Joe Hart is the first goalkeeper here in England.
"He had played two or three years at a very high (level of) performance.
"He can do it and we hope he will continue in the same way."
City, second in the table at the end of the year, will also continue without star striker Sergio Aguero at the Liberty Stadium.
The Argentinian was ruled out for up to eight weeks after suffering a calf injury in the win over Arsenal on December 14.
Pellegrini believes the 19-goal forward is making good progress and should return in the next month.
He said: "Sergio is recovering from his calf injury. I suppose in January he will be okay."
Playmaker David Silva is also not available on Wednesday after collecting his fifth booking of the season in the Palace game.
Defender Pablo Zabaleta - recently recovered from a hamstring injury - midfielder Yaya Toure and striker Alvaro Negredo, all rested at the weekend, are back in contention.
Pellegrini said: "Pablo played against Liverpool at the limit, so it was a risk of massive injury for him to play two games in 44 hours.
"Yaya Toure and Negredo were a little tired and will be fresh."
Striker Stevan Jovetic and defenders Martin Demichelis and Micah Richards are the other players sidelined.
City are well placed at the halfway stage of the season, a point off the top and through to the last 16 of the Champions League and Capital One Cup semi-finals.
With the transfer window to reopen, Pellegrini will consider whether to strengthen his squad.
Pellegrini said: "No, for the moment, we are not talking about that but we are always analysing what we need and what we don't need.
"We will see what we are going to do in the next days."