Celtic crashed out of the Champions League in the second qualifying round on Wednesday night when they lost at Midtjylland.
The club crashed out of the same stage of the Champions League qualifiers for the second season running and have not made it to the group stage for four years running.
Ange Postecoglou wants to bring in more players before the end of the transfer window and Rough admitted that Celtic have the finances to get out of a difficult corner.
But he indicated that he is not certain whether the club have the time or expertise to bring in the right kind of players this summer.
The former Celtic goalkeeper said on PLZ Soccer: “Celtic on the playing side are now where Rangers were eight or nine years ago.
“The only difference with Celtic is that they have got the money to get it right, but we don’t know who is using that money and what kind of stuff is going to come in.
“They certainly have to do it quickly.
“I know the manager is saying give me a month and that’s okay in footballing terms, but the horse has bolted as far as I am concerned.
“Celtic, three or four years ago, were a Champions League side but they are nowhere near that now.”
Celtic’s European hopes now lie on qualifying for the Europa League and they will take on Czech side Jablonec next week in the third round qualifier.