Two late tries from winger Warren Oliver and an earlier effort opposite wing Aaron Higgins meant that Westoe lost their first game in four.
The result leaves Westoe with 17 points exactly one third of the way through the campaign and sitting in the lower part of mid-table.
Nesbit feels that although Bromsgrove were probably deserving of the win, he couldn't falt his teams work rate in defence.
He said: "I think that the desire and commitment that we showed in our defensive work yesterday was brilliant.
"It is fair to say that they had much more possession than us and probably deserved the victory, but no way did the margin deserve to be as big as it was.
"We battled so hard and it was only in the last six or seven minutes when they scored the last two tries to take the game away from us."
It took only nine minutes for Higgins to get Bromsgrove off the mark as he went over in the corner, fly-half Bar Bartlett with the extras.
Two penalties within quick session from first Bartlett on 33 minutes and then Westoe scrum-half Matthew Mellish on 34 minutes made the half-time score 10-3 to the hosts.
Bartlett then added another penalty on 52 minutes before Westoe fly-half Jordan Carey ran over the line to close the defecit, Mellish converting with aplomb.
Just as the Shieldsmen were looking like they were getting back into the game, hooker Richie Thirkell was then sent to the sin bin for a technical offence on 62 minutes.
Bartlett added another three points from the resulting penalty.
The game was put beyond the visitors reach thanks to two tries in the last six minutes from Oliver and saw Bromsgrove move to within two points of Westoe in the table.
Nesbit believes that there were also some positives to take out of the game, but there is still a bit work to do for his team.
He added: "The attack wasn't really productive enough today for my liking. We didn't really create enough going forward.
"There were some positives to take from the game though because defensively we were good.
"It is still not quite what we're after but if we can strike a balance between our attack and defense and get a good combinationn of the two then we will be fine."

Westoe: David Haswell, Michael Potts, Lomi Fa'atau, Gareth Roberts, Ryan Beattie, Jordan Carey, Matthew Mellish; Gareth Nesbit, Richie Thirkell, Raymie Elliott, John Younghusband, Andrew Kirton, Haydn Richards, Rob Adair, Oliver Cracknell. Replacements: Dom Connolly, Grant Walker, Dan Rundle, Chris Judson, Joe McKenzie