Rangers went ahead in the 41st minute with a deflected opener from Heidar Helguson before the striker netted his second goal of the afternoon in the 60th minute and captain Adel Taarabt wrapped up the points with a late penalty.
Yet Mowbray said: "I didn't feel we were outclassed.
"They are a good side but for long spells, especially in the first half, we more than matched them. For an hour it was a decent performance.
"It turned out to be a disappointing afternoon but it could have been very different. Scott McDonald had a good chance in the first minute and had that gone in, who knows."
Source: PA
Source: PA