Watmore’s glaring 15th-minute error proved pivotal, although a draw between two sides with play-off ambitions was probably the right result.
Stoke star Tyrese Campbell will also feel guilty he did not convert his own opportunity in a lively opening period.
“You will talk about that missed chance and he would have been expected to score,” said Wilder of Watmore’s close-range effort that finished up hitting the back of the former Sunderland forward.
“But it wasn’t to be and they also missed a decent chance through Campbell.
“I enjoyed watching my team come into the backyard of a team who will be no doubt in the play-offs, and we have gone toe-to-toe with them.
“Overall, our performance was good and on another day we might have shaded a win in a tight game. We came to a side, who I said previously, was potentially the hardest match we had faced.
“However, the greedy part of me says we should have won it,” added Wilder.
“I don’t think it was a backs against the wall performance. We never felt we were massively under the cosh.
“I thought we dictated the flow and tempo of the game. When we had to defend, we defended properly in numbers.
“But it wasn’t a dig in, defensive performance. We weren’t playing an average Championship side.”
Stoke: Davies, Wilmot, Batth, Fox, Smith, Clucas, Allen, Vrancic (Ince 84), Tymon, Fletcher (Surridge 84), Campbell (Brown 80). Unused substitutes: Chester, Doughty, Bonham, Oakley-Boothe.
Middlesbrough: Lumley, Anfernee Dijksteel, Fry, McNair, Jones, Crooks (Bamba 71), Howson, Tavernier, Bola, Sporar (Ikpeazu 89), Watmore (Hernandez 74). Unused substitutes: Taylor, Payero, Lea Siliki, Daniels.
Referee: M Salisbury (Lancashire).