"We certainly had more possession in the second half than we had in the first," McCoist continued.
"We went in one down to a wonder strike, but I knew we had a chance."
The Ibrox side now face German side Werder Bremen in the last 16.
Manager Walter Smith says the Bundesliga's second-placed club could be a tougher prospect than Stuttgart, who they faced in the Champions League.
"We have a lot of time over the next few weeks to prepare for the big matches coming up in the cups," he said.
"It is going to be a difficult challenge playing Werder, they are a quality side.
"We lost to Stuttgart who are a good German side so we can expect a real test from Bremen as they're even further up their league.
"We will have to be at our best to beat them."
