After a slow start to the season, Liverpool are back on track and Sunday's 2-0 win over Southampton took them within two points of fourth-placed Manchester United.
Suarez's 31 league goals had helped Rodgers' side finish second in 2013-14, before the Uruguayan departed for Barcelona in a deal believed to be worth £75 million.
But Allen believes his team have improved without Suarez.
"At the start of the season we talked about how losing Suarez was going to have an affect but now we have overcome that," the Welshman said.
"It took us a little bit of time because the injury problems we had were not ideal.
"We are certainly back up to that level now and, if anything with the different system we play this season, we might even have taken a step forward.
"We have a more clinical edge now than we did at the start of the season. That’s grown with our momentum and picking up points – it tends to happen that way.
"We would have wished it was earlier than it has been, but we’ve still got plenty of time left this season to really go on and achieve things."
Liverpool were somewhat fortunate in their victory at Southampton, with the hosts having three first-half penalty shouts turned down.
Allen appeared to bring down Filip Djuricic for one of those, and while the midfielder admitted to not getting the ball – he understood why Kevin Friend did not point to the spot.
"If I am being honest I didn't get contact on the ball, which was disappointing because I felt I could get it but missed it," he said.
"I didn't really take him down either so it is one of them where my heart was in my mouth a little bit but at the same time I can see why it wasn't given."
