For the second game in a row, Boro threw away maximum points from a winning position when Paul Taylor's 81st minute wonder strike cancelled out Bates' opener.
It came seven days after the Teessiders had twice thrown away the lead against Blackpool at the Riverside.
A win at London Road would have put Boro level on points with third-placed Cardiff City and although Bates admits it was frustrating not to return to Teesside with a win, the centre-back insists bringing a point back was better than nothing.
He said: "Peterborough are a good team and they had to work hard to get a result. Every point matters and they'll add up towards the end of the season.
"We had a few chances, we could have scored at least one more and it's disappointing that we didn't take it.
"We know we should have won the game but it wasn't to be so we move onto Tuesday and it will be a big game for us against West Ham."
Last season, Boro were guilty of losing several times in the closing stages of games and Bates believes the fact his side were pushing for a winner despite conceding a late goal signifies how much improvement has been made.
"I don't know if it's in relation to what's happened in the last four years - defeats, relegation and that mindset of not picking many points up and not used to being one nil up in games, but I think we have improved since last year," Bates said.
"At times we were one-nil up or drawing and lost games in the last five minutes and we didn't do that today. We looked like a team that could win at the end but we'll take the positives out of it, we'll learn and improve on protecting leads."
It was perhaps even more disappointing that Boro could have closed the gap on leaders Southampton and put more daylight between the sides below them had they won at London Road, but Bates insists it is too early to be looking at the table.
"I can't believe we're looking at results already," Bates added.
"It's not even December yet! I'm not looking at the table as it is, I'll look at it in the last five or six weeks of the season.
"There's still plenty of time for teams to move up and down the table but we just have to focus on picking up as many points as we can to keep ourselves in this position."
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