The show has always established House Lannister as by far the most powerful house in Westeros - they even have Tyrion in the episode commenting on how they have been the true power in Westeros for a long time. They are the richest, can raise the biggest army and have the best equipped and most highly trained forces. Not consistent with the books as the Westerlands is one of the smallest of the 7 kingdoms while the reach is huge and can raise a far larger host, but there you go.
By comparison the Tyrells are established on the show as being the number 2 house right from the beginning, they are the second richest, can raise the second biggest army, and now according to Olenna can't actually fight that well as it's never been their forte. I think that's all the explanation they're gunna give for why the Tyrell's lost other than Tarly and possibly other Reach lords siding with The Lannisters.
Also, the show seems to have decided that the War of the five Kings hasn't had much of an impact on The Lannisters forces. Unlike the books where they're on their last legs