Liverpool were on a run of 13 Premier League wins until they suffered defeat at the hands of Manchester United, leaving them five points adrift of the Champions League qualification places.
Defeat at third-placed Arsenal on Saturday would be a huge blow to their aspirations of returning to Europe’s elite for a second successive season.
“We’ve made it difficult for ourselves because of our last performance and result, but it’s certainly achievable,” Rodgers said of their top-four chances.
“Over the course of the last three months, apart from the last game, we’ve performed very well and we have got results.
“I think people might look at it (the trip to Arsenal) as a must-win game. For me, it is a must-perform game, we want to perform well and we know that when we do that we’ve got every chance of winning, whether that’s at home or away.
“We’ve had a long two weeks, it’s probably one of the few games where after the international break we’ve had to suffer a little bit, because we didn’t perform and lost, but there is extra motivation there to get something from the game and that is something that we clearly want to achieve.
“These final eight games are going to be exciting games and there is still every possibility for us to make the top four.”
An inability to keep possession against United was a key factor in their loss, and Rodgers has spent the international break assessing why his side could not hold the ball.
“The key for us in the first half against Manchester United was that we didn’t keep the ball well enough and, positionally, we were never in position to receive the ball and press the ball,” he said.
“We’ve talked about that, we’ve analysed that and we’ve worked on that; in order for us to maximise how we’ve been working we need to keep the ball better and be technically better.
“That’s a huge part of our game, and it’s Arsenal’s game. But for us, we’ll go there and tactically we are very clear on the idea of the game and we need to get something from the game, that’s clear.
“We’ll be going there looking forward to the game and really motivated to get back to winning again.”
Liverpool have been boosted by striker Daniel Sturridge’s return to training after a hip injury, while fellow England international Adam Lallana is also expected to be fit despite pulling out of the national squad.
However, they will be missing centre-back Martin Skrtel and captain Steven Gerrard who are both suspended for three matches.