Shane Duffy's last-minute goal against Bulgaria in September is the last goal Ireland have mustered, with five blanks in succession leaving plenty of questions over Kenny's efforts to transform the team's style of play.
Former Ireland captain Keane admitted Kenny has a tough job on his hands to find a winning formula with a team lacking goals, as he believed more could have been done to stop England's goals as they beat Ireland for the first time since 1985.
"It probably doesn't help that Ireland's best player at the moment is a full-back in Seamus Coleman," Keane told ITV Sport.
"This is very hard work. Ireland were way off the pace. England would have had tougher training days than this, so there is a long way back for this team.
"There are a lot of good solid pros in the squad, but none of them are pulling up any trees at club level. So many of them are playing in the Championship and that bit of quality is missing. You need that to win matches at international level.
"They started okay in the first 20 minutes, but you felt every time England went forward they would do something.
"(Shane) Duffy is having a difficult spell club wise and Harry Maguire looked like he wanted it a little bit more. When the ball comes into the box, you ask who wants it more.
"Then on the second goal, Jeff Hendrick has got to get tighter. At this level, the idea that players can be two or three yards away from someone like (Jadon) Sancho and get away with it is not good enough."
Keane's fellow ITV pundit Ian Wright suggested teenage Norwich striker Adam Idah showed signs of rawness against England, as he failed to show an eagerness to get into the box when Ireland had a couple of half-chances on the break in the first half.
"He is a young guy and it is the kind of thing you want to see him doing as a forward," stated Wright. "You want to see him busting a gut to get into the box and if he gets in there, he could get picked out.
"At times, he got himself into nice positions, but he needed to be moving more. At this level, you have to have that desire to get into the box.
"You want to get into the box as soon as you can and at this level, he has some good opportunities to get in there and have a chance to score."