The Light Blues finished 39 points behind Celtic in third place last season and this campaign got off to a terrible start with Europa League defeat against Progres Niederkorn of Luxembourg.
Wallace admits they cannot ignore Celtic’s strength following their undefeated domestic season but he believes they must aim high.
Speaking at the launch of the Ladbrokes Premiership campaign at Hampden, the left-back said: “Obviously we take last season into consideration. We are well aware of the task and we are well aware of how far off it we were.
“But our mindset won’t change as Rangers players, and that’s to win every single game home or away, and win every competition that we enter.”
Rangers have made nine summer signings and spent more transfer money than Celtic so far and Wallace knows that a strong title challenge is a must.
“Irrespective of signings, irrespective of the cost, that has to be the aim for us,” he said. “We have to obviously recognise what happened last year and be realistic about things, but it’s not going to change our focus as Rangers players.
“We can’t settle for any less than that, it has to be the target. If we approach every game with that mentality, we will definitely finish off stronger than we did last season.”
Manager Pedro Caixinha joined in March but Rangers drifted further behind Aberdeen in the race for second, and the brief European campaign did little to endear the Portuguese to the Ibrox support.
And Wallace admits there is pressure on them to start the season strongly when they face Motherwell at Fir Park on Sunday.
“Absolutely, there is always going to be pressure watching Rangers, even if it’s a friendly,” the former Hearts player said. “It just becomes the norm and it’s about how to handle that and how to respond to situations like the European exit.
“We have managed to do that. We are feeling good. We recognise it’s going to be a difficult game, they have some momentum from their League Cup campaign, but we are going to go there and try to win the game.”
Rangers gave their fans some encouragement by recording wins over Watford and Sheffield Wednesday and drawing with Marseille in an impromptu pre-season campaign which was hastily arranged following their defeat in Luxembourg.
Wallace said: “We suffered a humiliation in the European campaign but it was about how we responded to that and, more so in the last 10 days, there’s definitely been a bit more positivity generated amongst the players, and a bit more belief.
“Of course, four or five days after you are still hurting. But the demand at the club is you have to quickly get back on it, and that’s back on the training pitch, and you have to forget about it.
“While it still hurts, you need to use it as a lesson. Guys that have came to the club feel the demand and the scrutiny you are going to receive if things don’t go well.”
Wallace added: “Of course, we are not getting too carried away. We recognise there’s a long way to go for us. We are still learning about each other and gelling as a team but there has certainly been a better end to the pre-season than we started and we are all raring to go next Sunday.”