Rangers enjoyed the lions-share of possession, according to Holloway, but came away from the south coast empty handed after a defensive lapse allowed Warren Feeney to nip in to give Bournemouth what was to be the decisive goal.
Despite the loss being Rangers' second in a week - having exited the LDV Vans Trophy at the hands of Southend United - the Rangers manager remained positive about the hard work that his players had put in, and the support that the travelling fans had shown right till the end.
"I am devastated with the result. I don't think we deserved that at all. Second half we dominated - you wouldn't have known who were the home team out there today.
"I've been in this game a long time and I time and I think my team are looking a very good team, and I think that was a very good away from home performance considering who we've got out at the moment."
With players like Gareth Ainsworth, Marcus Bean, Richard Edghill and Kevin McLeod currently out through injury, the Rangers boss feels that his squad's depth is being stretched to its limit.
"We need them. It's a squad game - and we're running on empty a bit at the moment. I'm not making excuses, that's just how it is.
"I want my players to be under pressure to keep their place, not under pressure to keep playing.
"The lads did an awful lot of good work out there today - and one lapse cost us.
"It just goes to show that we are not too big to get beat."
And with results in the top half of the table generally going in favour of the higher placed clubs, the Rangers boss was quick to dismiss suggestions that the Second Division is becoming a race between the top few clubs.
"Look at where we were last year when we put a run together. How can this be a three horse race?
"I'd be doing us a disservice if I thought that."