"They both have tears," said Redknapp. "It's difficult to know how long they will be out for."
Redknapp also had to take off Jake Livermore, who suffered a cut lip in a clash with team-mate Younes Kaboul.
Both bloodied players had to leave the field to receive treatment and the incident left Spurs with nine men on the field for a short period of time.
Despite the problems in personnel, with midfielders Scott Parker and Aaron Lennon already out because of injuries, Redknapp's side managed to grind out a victory over the Baggies thanks to a second-half goal from Jermain Defoe.
Redknapp credits 'tough' West Brom
The result means Spurs move to 42 points, three behind Manchester United, with leaders Manchester City on 48.
And Redknapp stressed England international Defoe, making a first start in over a month, was still an integral member of his squad.
"Jermain's a goalscorer and always likely to pop up and nick a goal like that," he said.
"He's a good player. I've signed him nearly everywhere I've been. I signed him as a 14-year-old kid."
Redknapp's side created very few chances in the match against a Baggies side who defended brilliantly and were without the attacking impetus provided by striker Shane Long and midfielder Chris Brunt.
"It was a tough game for us," added Redknapp.
"They had injuries so Roy [West Brom manager Hodgson] set them up to defend and they were tough to beat. They didn't leave too many gaps at the back, but the little man managed to stick one away.
"We didn't create the number of chances we normally do. Full credit to them, they made it hard."
Hodgson shrugs off fixture congestion
West Brom created little but put the home side under pressure in the final 10 minutes.
"With a modicum of good fortune we could have come away with something," said boss Hodgson.
His side had a day less than Tottenham to recover, having played on New Year's Day and Hodgson said the club had requested the fixture be put back a day.
"We're not the only team to play twice in three days," conceded the former Fulham and Liverpool boss.
"We tried to have the game moved to Wednesday, which Spurs were happy to see done too.
"I'm not sure why weren't allowed to do it. Who knows what goes on in the discussions about fixtures, although it would not have changed the team selection, because those injured would not have been fit anyway.
"However, all the players who came in tonight went away knowing that they showed the manager what they could do."
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