Graeme Murty will remain as interim manager of Rangers "at least until the end of the year" after the club's failed pursuit of Derek McInnes.
Murty, the club's Under-20s coach, has guided the side to four wins in six games in his second spell as caretaker.
"The manner in which he has approached this task is a credit to himself and the club," said a Rangers statement.
It said the club "will only appoint someone in whom we have full confidence and who feels he is ready for the job."
Rangers were refused permission to speak to Aberdeen manager McInnes after making an approach on Tuesday.
After McInnes spent two days "weighing up the opportunity", the Dons announced on Thursday that he will remain as manager.
Rangers sacked Pedro Caixinha six weeks ago, with McInnes their preferred candidate to succeed the Portuguese.
Last week, Rangers chairman Dave King told the club's annual general meeting that progress was being made with a shortlist of candidates, saying: "We should have something to report shortly."
But after McInnes opted to stay at Aberdeen, Rangers issued a statement on Thursday evening defending their handling of the process to appoint a permanent manager.
It read: "There has been a great deal of media speculation regarding the appointment of a new manager. We assure all supporters that they will be the first to know when we are certain we have someone with the correct qualities required by our club.
"The chairman made it clear at the AGM that the club did not consider there to be an outstanding candidate among those who had applied for the position and the club was therefore considering managers currently under contract. This requires permission from their present clubs.
"The position of Rangers manager requires an ability to win football matches and the mentality to cope with the demanding off-pitch environment that goes with being the Rangers manager. This is a critical aspect of our assessment of any candidate during the interview process.
"After the two games against Aberdeen, we requested permission to engage with their manager to assess his readiness and willingness to consider the Rangers position. This was declined.
"We were subsequently made aware by Aberdeen's statement that, at this stage in his career, it would be best for him to remain in his current post.
"We endorse that position because moving to a massive club like Rangers is a big step with concomitant risk.
"We continue to consider candidates but will only appoint someone in whom we have full confidence and who feels he is ready for the job.
"In the meantime, we have great confidence in Graeme Murty, who will continue as interim manager at least until the end of the year. The manner in which he has approached this task is a credit to himself and the club."