Middlesbrough hadn't dropped a point on their travels since they were beaten 3-1 at Turf Moor last April and Mowbray said after the game: "We were all very conscious of that before the game. The last time we lost a football match was here and we were determined not to let it happen. We scored two good goals and kept a clean sheet and the defence and goalkeeper were excellent.
"Good players, hard work and organisation is a formula for winning football matches and great credit to them today, they did the job in all departments. Football's all about the team believing in what you ask them to do. If they don't believe it, it's difficult. Hopefully they're putting into practice, results are good and they believe they can win every game."
Boro have been relying on the strikers for goals but today they came from midfielder Nicky Bailey and left back Joe Bennett. Mowbray added: "You have to score 70 or 80 goals to be successful in this league and you have to get them from all over the pitch, you can't just rely on Scott and Marvin.
"I'm delighted for Joe, last season he looked every inch a top Premier League footballer and while he hasn't had a flying start this time, I thought he was excellent for England U21s and again for us today.
"Nicky Bailey scores a lot of goals in training but I can't believe he scored 13 goals two season running for Charlton because he never crosses the halfway line in games! He believes he can score goals but he does a fantastic defensive job for us. He has an instinct for spotting danger and snuffing it out and hopefully he'll keep doing that for us."
Eddie Howe saw Burnley's run of home league games without a win stretch to five with this defeat and with it the first defeat on home soil since Ipswich won 2-1 in early April.
"We've no complaints because I thought it was a poor performance from us," Howe said. "In previous weeks we have been unlucky in deserving more from the game.
"Today I didn't think we did. We were beaten by the better team and in the end it was our worst performance of the season by a long way. We left our performance on the training pitch and it's difficult to work out why.
"We conceded quite early with a poor goal and then they got men behind the ball and we found it difficult to break them down. They were very organised, dropped deep and defended very compact. Away from home that is proving to be a very successful system for them with the results they have had recently."
He continued: "On the back of the win against Derby I decided to keep the same team because I was looking for a similar performance, but a number of players, for whatever reason, didn't perform today.
"It's concerning for us that it was quite a number. It's very rare that you get so many off colour - big players too, who we need to perform to have a chance of getting results.
"We felt we weren't in control in the first half and we had to change something. We decided to match them up and go man for man, not let them have an 'out-ball' and a spare man. I wanted to press them, get the crowd on our side and try to swing the game, but we never really, at any stage, looked like breaking them down, which is the most disappointing thing.
"Turf Moor is our bread and butter and where we need to perform week in and week out. We need to get the crowd with us and we need to be able to play here. At the moment we are struggling a little bit with that and it's obviously a concern."