Danny Graham opened the scoring for the visitors before two goals in 12 minutes from Scott McDonald and Andrew Taylor gave Boro three valuable points.
Mowbray said: “It is a good cushion but that doesn’t mean anyone here will be relaxing.
“It is a big gap, we know that, and some of those teams behind us now need to win three games to close the gap on us and with every week they have fewer games to do that in.
“But we know what this game is like and what this league is like and we can’t take anything for granted. We know there is a long way to go.
“We’ve got a break next week but then we have a big April with eight games and we know we have to keep our standards high and have to keep picking up points.
“But I thought we deserved it. We played well, we worked hard and we kept going. I’m pleased.”
Watford manager Malky Mackay accepted Middlesbrough did enough to collect the three points.
Mackay said: “Boro deserved it.
“That was probably the first time this season that over the 90 minutes we haven’t given as good as we got.
“It was disappointing because with other results it was a chance missed to close the gap on the play-offs but we have eight games left and we will give it our best shot.”
Mackay was bemused with the referee’s decision to send him to the stands for stepping onto the pitch to trap a ball that was rolling out. Mackay said: “It’s probably the only time in my career I’ve been a yard too quick.”
Middlesbrough: Smith, McMahon, Rhys Williams, Grounds, Bennett, Robson, Bailey, Arca (McManus 84), Taylor, McDonald (Zemmama 88), Emnes. Unused substitutes: Ripley, Haas, Kink, Smallwood, Tavares.
Watford: Loach, Thompson (Bennett 46), Taylor, Mariappa, Hodson, Cowie, Jenkins, Eustace, Buckley (Sordell 68), Deeney (Weimann 79), Graham. Unused substitutes: Gilmartin, Mingoia, Whichelow, Smith.
Referee: Gary Sutton (Lincolnshire).
Man of the match: Andrew Taylor.