Rotherham were on course for a famous win which would have done wonders for their battle against the drop after a fine opening hour.
After coming in at the break with the score at 1-1, a two-goal salvo from Richie Smallwood and Matt Derbyshire within nine minutes of the restart had them well on top.
Derbyshire almost made it 4-1 only for Lee Grant to produce a fine save and from the resulting corner, the Rams broke and made it 3-2.
The joint-leaders then snatched an equaliser and despite taking pride at their display, Millers boss Evans was disappointed as his side moved four points clear of the relegation zone.
“What an advert for Rotherham United being (in) the Championship,” the Scot said. “There’s tinges of great disappointment being 3-1 up.
“We got a point but we have come across the best team and manager in the division.
“They have laid siege, there is some sloppy defending from us, the second and third goals could be averted.
“We are immensely proud of them. We have got a point and we are a bit disappointed. Every player gave me everything, I can’t ask for any more, but we are disappointed.
“We will take a point and we will be a coupon buster for most people around the country. We have taken a team which will be in the Premier League right to the wire.”
Doncaster Rovers moved into the top six in League One for the first time this season thanks to a 2-1 win over Crewe, courtesy of Richie Wellens’ last-minute strike.
Rovers had trailed to George Ray’s early goal but Dean Furman scored a similarly scruffy goal to level matters on the hour mark, before Wellens struck in the last minute.
Doncaster had 17 shots at goal in a dominant second period, and Dickov said: “We were disappointed to concede a sloppy goal and in the first half it felt like Walsall all over again.
“So all credit to the lads. They showed massive character and a lot of confidence and belief to get the result.”
Like Rovers, Sheffield United made it three wins in a row to consolidate their place in League One’s top six.
January signing Matty Done made it four goals in three games with the winner in a 2-1 victory at Notts County.
Blades boss Nigel Clough said: “We couldn’t have got Matty Done in the summer. We had to be patient because they’re aren’t many like him around.
“And our first goal was superb. It’s the old adage. Give the ball to Jamie Murphy and he’ll produce something like that.