Nathan Delfouneso’s late goal – scored five minutes after he entered the pitch as a sub - looked to have sealed a deserved win at Valley Parade.
But Danny Rowe crashed home an equaliser in stoppage time at the far post to ensure both of League Two’s form teams preserved their unbeaten runs.
Evatt admitted his side should have been out of sight after dominating long periods of the second half.
“I thought my team were outstanding, I’ve got to say, I think that’s the best we have played on this run considering it’s against a side that has won five on the trot,” he said.
“We dominated the game. The slight criticism is that we should have been out of sight but that’s it. When it stays at 1-0 and they are sending the keeper up for desperation – they got a couple of fortunate ricochets and it fell to the lad who put it in.
“My players were outstanding. I can’t ask for anymore, I don’t think anyone can. We deserved to win the game.
“They are disappointed in there but I just said to them they have to hide that disappointment, get rid of it, get the music on, because if we play like that again I fancy us to win more than we lose.
“Hopefully everyone has seen that. We dominated the game, some of the passing and rotation, our counter-pressing on rotations was magnificent. We need to build on that and if we can repeat that over 13 games then we have got an excellent chance.”
The Bolton goal came via a shot from former Bradford man Eoin Doyle which looped up off keeper Sam Hornby before being guided over the line by Delfouneso.
There was some confusion at first over which player would claim it – but Evatt felt it was just reward for the second-half display.
“Nathan scored the goal but it was great work from Doyle as well. The only disappointing in the whole day was the final third decision or finish,” he said.
“Their keeper made one good save and they threw their bodies in front of everything, had one off the line. The goal was coming.
“The only slight critique is that we should have been out of sight but if we play like that for the rest of the season I don’t think there will be many disappointed Bolton fans.”
Rowe’s goal did put a slight dent in a decent day for Bolton but Evatt won’t allow his players to dwell on any disappointment.
“When it’s last minute and they are a big, physical team, anything can happen,” he said. “They got a lucky ricochet from a second phase and the guy toed it back in and it fell for Danny Rowe at the back post. It could have gone anywhere but sometimes that happens in football. I’m just happy with the performance, that’s what I am concentrating on.”