The veteran rockers paid tribute to Entwistle, who died of a heart attack in 2002, and praised his replacement, Pino Palladino, while Townshend also spoke of his sadness at losing Moon, who passed away following a drug overdose in 1978.
Townshend said, "Replacing John Entwistle was a hard job, as he had such a unique style. But this guy is probably the best bass player in the world today... You'll have seen pictures of Keith Moon on the big screen behind us tonight. When I see them behind me, I miss him terribly..."
Daltrey went on to dedicate 1965 hit The Kids Are Alright to Weller, who performed before The Who at the gig in Hyde Park in the U.K. capital.
He introduced the song before being told it was the wrong track, saying, "This song is for a special friend. I don't usually do requests, but this is for Paul Weller, who asked us to play it," when Townshend interjected, "I thought we were playing something else."
Daltrey replied, "I f**ked that up. I write these setlists the night before a show and always forget them. That time of my life when I forget everything is sitting on the doorstep."
The Who and Weller are both set to take the stage at Britain's Glastonbury festival on Sunday (28Jun15).