Warriors looked set to record a key home win after full back ace Chris Latham scored a try with less than 20 minutes left to add to an earlier penalty try.
But late drama saw a high tackle awarded against Warriors on David Lemi and visiting fly half Ed Barnes stepped to level the scores on an afternoon of high tension.
"We let them back into the game and we have got to kick ourselves for that. I am angry at conceding that late penalty and I have told the players that," said Director of Rugby Ruddock.
"If we are serious about being a top side in Europe we have got to stop things like a quick throw-in happening, that is where it all started for them.
"That was my message to the players - we should have closed that off. We stopped the initial chance by playing a chase and filling the space but then allowed them back into the game.
"But from there they got the high tackle, which talking to a few people in the changing room they felt it was debatable, but we have to accept it. That is what happened and well done to Bristol for snatching the draw.
"The boys feel it was harsh but there is a quality referee out there and we have to accept his decision.
"We did enough to win the game and I thought we were the better side. Bristol battled hard and scored two good tries from their two opportunities. Other than that they didn't really have too many other chances.
"But in fairness they closed us down and stopped us creating too much. But overall we had the better of the second half and should have got the result based on quality possession."
Ruddock admitted the clash had been a real physical and bruising encounter and paid tribute to the way his side had battled hard under intense pressure.
He said: "It was a good battle and both teams looked as though they were nervous at the start, there was a lot up for stake at the start. Both teams played a game of chess and a kicking game, nobody wanted to make mistakes in their own half.
"When Dale Rasmussen got sin binned that allowed Bristol to have the opportunity to put some pressure on us and they got a nice try as a result of some good play. Whether we would have stopped them with a man more I don't know but it was a big score for them. Until then we hadn't looked in any danger at all.
"Our penalty try at the start of the second half was then they had a man in then sin bin. That evened things up.
"We thought we had done enough with the fantastic try from Latham after Bristol had scored before. We thought we were going to close out the game but unfortunately we didn't do it, we had a couple of opportunities.
"Bristol showed some good thinking with a quick throw in and from that they got the penalty to snatch the draw. You have to give a lot of credit to Bristol, they battled and battled, it was a cup final for them. They made it very difficult for us."
The defeat means Warriors now face a huge league clash with Newcastle Falcons in seven days time and Ruddock admits the game in the north east would be a big one.
"We have a massive game next week with Newcastle and if we can do the business we can carry on pressing on," he said.
"Yes, we are very disappointed, we make no bones about that, but it was always going to be the narrowest of margins here today. We knew Bristol would be scrapping for their lives.
"But if you out this result into context, this time last year we didn't have a win. It is another two points gained and they are always valuable."