The Whites won their first game in seven in the Championship clash with Neil Lennon's side on Saturday.
Two goals from Mirco Antenucci helped the Whites to their first win in seven games in all competitions, and went some way to repairing some of the damage that was done during the team's shambolic performance in the recent 4-0 defeat to Brighton.
And Evans conceded that he would have understood if the support had not been there against the Trotters following Monday's mauling, so was thankful to those who were at Elland Road.
"To the people who did turn up, we're very grateful. We possibly didn't deserve support, especially from the ones who went down to the south coast," he told the Yorkshire Post.
"But we were really hurting and we've got a fine win."
With United's play-off hopes almost completely in tatters, there appears to be a feeling developing that the club's season is practically over as it will probably require just a few more wins to guarantee their survival, while it would take a sensational run for the team to go near the top six.
So with thoughts already turning to the summer, supporters could be forgiven for letting their frustrations boil over, especially as this is arguably the fourth consecutive campaign where the team have fallen away before the play-off race has even really begun.
But with safety not quite assured just yet, Evans will be hoping that the supporters continue to come through the turnstiles and inspire the team to end the season strongly.