The Baggies went a goal down in the first-half from Boro wing-back Isaiah Jones and were frequently cut apart on the opposite flank by on-loan Wolves defender Ryan Giles.
However, Albion seized the initiaive after half-time as new recruits Jed Wallace and John Swift combined for the latter to level and grab a point at the Riverside.
And Bruce said: “I thought we started well enough but we didnt really recover after they scored until half-time. The second half was much better and I was pleased with the reaction but the 25 minutes after they scored was difficult for us.”
And he added: “What you say in the dressing room has to stay in the dressing room but there were a few home truths.
“I think they just needed reminding to play with a bit more intensity and second half was chalk and cheese – that was evident for everybody to see.
“Arguably we could have gone on to win it, but Middlesbrough, for me, will be there or thereabouts.
“First game of the season there’s a bit of a feel-good factor around and there were times in the first half when it was difficult but we got through it.
“If we keep what we showed in the second half then we’ve got a chance.”