Sai Masu Gida played out a 1-1 draw with Henry Makinwa's men in their Nigeria Professional Football League Matchday 26 encounter and now sit eighth in the log.
"We were close to getting the three points but ABS took their chances because we gave in late in the match and we had to settle for a point," Alimi told Goal.
"The point gotten in Ilorin was a very good one for us because first, we aren't going back to Kano empty handed and if you know what it means to pick points on the road in the Nigerian league then you will appreciate our effort.
"Every team puts in extra effort at home and that to a large extent makes it a lot difficult for the visiting team but a determined side like Kano Pillars don't give up just easily. We fight till the end and in this case, we picked up a point.
"We are still on track with our set goals of making the top three at the end of the season, we are a big team and it's expected that must win a major trophy every season.
"We believe we still can and we shall continue to work towards getting it."