First assistant Martin Jol takes charge for today's visit of Charlton to the Lane and the Sporting Director reported that an announcement on the management structure will be made on Monday.
"Of course it is a disappointment that Jacques has gone," said Frank this afternoon. "I knew from him from a while ago that he had problems so it was not a big shock.
"We started here this summer with everything new, a lot of new faces on and off the pitch and we were and are very ambitious and keen to do a good job. Let's be clear, I had confidence in everything here and still have that confidence. We have to work hard and we will.
"We have good players and good back-up with our technical staff. I think it is very important for the fans to know we will handle this in a way that is good for Tottenham.
"This is totally a decision that has come from Jacques himself. I have been asked about the timing, but we should never talk about the timing when it comes to personal problems - we hope everything goes well for Jacques and he overcomes these problems as quickly as possible."
Frank also believes the team can also overcome the recent dip in Premiership form and get the season back on track.
"We are only just into November and there are a lot of games to go. We have the players, we will continue to work hard and we are looking at the possibility of strengthening our squad.
"I feel we have done more than reasonably well with our signings from the summer, they are still fitting in and are still young. We have done a little less well in the last couple of weeks but it is all in the context of the season, you will have ups and downs.
"It is now very important to do something this week, we have three big games and it will be good."
The squad was not the only department bolstered during the close season with much expertise being added to the coaching staff and, for this reason, Frank has every confidence that the effect of the departure of the Head Coach will be minimised.
"The staff is very strong and that is why I had no hesitation at all in announcing that Martin would take over for the Charlton game. He has held the same position in Holland for more than ten years at the highest level and it is not a problem at all. He has good support behind him as we have a good technical staff.
"The proper way to go forward now is for me and the board to sit down over the next couple of days and go through everything to ensure we do the right thing. Then we can clarify everything as quickly as possible for the supporters.
"I am still very confident we will do well.
News of Jacques departure was met with many a conspiracy theory by the morning press, suggesting possible internal clashes and pay-offs. Frank categorically denies the reports.
"It is crystal clear, we are a public limited company and everybody can look into our books. If a coach asks to go he will be paid for the job he has done up to today. This should clarify everything for everybody - there has been no pay-off.
"Jacques has made his decision and I think it is a little bit sad because the image of Santini should be held high. This was a personal problem and not a football problem.
"Jacques did well and got us off to a good start. In four months he did very well with the language and did his best for the club."
Frank Arnesen insists our aims and ambitions for this season are in no way altered following the departure of Jacques Santini on Friday.