All three defenders missed the clash with City at the Tottenham Hotspur Stadium, with the head coach providing the latest updates ahead of next Saturday's Premier League trip to Manchester United.
Frank revealed that Micky van de Ven, who also missed the midweek Champions League win over Eintracht Frankfurt, was unfortunate not to feature against City.
The centre-back is expected to return for the Manchester United game. "Micky is a minor one. I fully expect him to be available for Man United, he just couldn't make it for this game unfortunately," Frank explained.
Kevin Danso suffered a more serious setback. The Austrian defender hyper-extended his big toe during the Frankfurt match, causing a snapped ligament. Frank added: "Kevin, another, I think quite unlucky one. He hyper-extended his big toe when he landed on the foot of an opponent against Frankfurt. The ligament snapped in the big toe. It's extremely unlucky.
"We don't know the length of it yet, but we have an appointment next week to clarify that."
Djed Spence also missed the City clash with a calf injury. Frank was cautiously optimistic about the full-back's recovery, saying: "Djed has a minor calf injury. I hope Djed is not out for too long."
Tottenham will monitor all three players closely this week as they prepare for a tough Premier League test at Old Trafford, with defensive options limited.
Pep Guardiola cut a frustrated figure after Manchester City let a 2-0 advantage slip in a dramatic 2-2 draw at Tottenham, with the City manager openly questioning the decision to allow Dominic Solanke's first goal to stand.
Aston Villa's title momentum took a hit on a dramatic Premier League afternoon that also saw Nottingham Forest edge closer to safety and Crystal Palace extend a frustrating run.
Michael Carrick has said winning late at Old Trafford was "the best feeling" after Benjamin Sesko's stoppage-time goal sealed a dramatic 3-2 win over Fulham and made it three straight victories for Manchester United.
Dominic Solanke scored twice as Tottenham recovered from a two-goal deficit to draw 2-2 with Manchester City at the Tottenham Hotspur Stadium, a result that left the champions six points behind Premier League leaders Arsenal.
