A James Tavernier goal in the second half was the difference as Rangers beat Aberdeen 1-0 at Hampden Park to life the first domestic trophy of the season in Scotland.
Rangers have grown strength to strength since Philippe Clement took charge of the team from Michael Beale and are also within touching distance of Celtic in the Scottish Premiership title race.
Miller conceded that Clement and Rangers deserve credit for the results but stressed that they are not a great side who beat Aberdeen in the final.
He insisted that the first half of the cup final was poor and while Rangers were the better team in the second half, Aberdeen offered very little at the other end until they got desperate towards the end.
The Aberdeen legend said on BBC Radio Scotland: “Rangers and Philippe Clement is absolutely 100 per cent as far as results are concerned.
“But do not tell me that is an outstanding Rangers team.
“It was a poor first half, it got a little bit better in the second half and Rangers were certainly the better team in the second half.
“Aberdeen quite simply didn’t offer enough in the closing moments when it was desperation time.”
If Rangers win their two games in hand, they will go above Celtic in the Scottish Premiership table.
