A goal from Martyn Woolford in stoppage-time secured a 1-1 draw at Glanford Park.
Leicester took the lead after just three minutes through Martyn Waghorn and the visitors enjoyed a dominance of the match that should have seen them go on to score more.
But, while recognising his side rode their luck, Adkins hoped the result could be a turning point.
"After four successive defeats, this was an important result for us," he said.
"We made life difficult for ourselves by giving away a poor goal in the opening few minutes.
"Leicester are a difficult side to break down and don't concede many goals, but we showed great spirit, we kept going until the end and finally got the goal we deserved."
Nigel Pearson, the Leicester boss, was not downbeat despite having seen an away victory snatched from his grasp.
"I am disappointed because we had chances in the first half to score more goals, but I am not going to have a go at my players because this was another good away performance," he said.
"There was just one ball into the box that we did not deal with - and it has cost us. We have scored a lot of late goals to win games in recent weeks, it was somebody else's turn to do the same to us."