Boro remain eight points adrift of the top six with 10 games to go, the first of which is a home clash with Preston on Tuesday night, and Warnock wants his side to build on Saturday’s victory.
Warnock was impressed by the way his side brushed Stoke aside once Grant Hall had put them ahead in the 21st minute.
The impressive Paddy McNair added the second five minutes before half-time before substitute Nathaniel Mendez-Laing wrapped things up in the 88th minute.
Warnock said: “We had to win. I said to the players we have to try to get wins on the board and I thought once we sorted the first 10 minutes – the system was cock-eyed, we changed completely – we were on our game.
“We dominated certain areas, broke quickly. Even in the second half we broke at pace and could have had a few more.
“Marcus Bettinelli made two important saves, it might have been nerve-wracking if they had gone in. We just have 10 games left and we have to try to win every game. We are capable of winning every game, but we are capable of losing them too.
“There were some massive pluses today. We looked strong once we changed. Paddy getting that freedom and he finished really well for the goal. Mendez-Laing, I couldn’t have asked any more from him.”
Middlesbrough: Bettinelli, Fry, Hall, McNair, Spence (Mendez-Laing 82), Howson, Morsy, Bola, Kebano (Johnson 65), Bolasie (Fisher 66), Akpom (Assombalonga 77). Unused substitutes: Archer, Watmore, Saville, Coulson, Coburn.
Stoke City: Gunn, Smith, Souttar, Chester, Norrington-Davies (Vokes 67), Mikel, Allen, Brown (Tymon 46), Powell, Clarke (Matondo 64), Fletcher. Unused substitutes: Batth, Davies, Oakley-Boothe, Thompson, Forrester, Norton.
Referee: Andrew Madley (West Yorkshire).
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