The Ibrox captain believes the Scottish champions broke the bank to recruit new manager Brendan Rodgers because they fear a major title threat from newly- promoted Rangers.
Preparing to kick off a top-flight season for the first time in four years, Wallace is convinced Warburton has created a side which is capable of winning major trophies.
“The fact they [Celtic] have brought in a manager of that calibre [Rodgers] is due out of respect to what we’ve done,” said Wallace.
“They’ve had a look at the semi-final result last season, what we did throughout the season and how we’ve been moving forward as a club and the steps we’re making.
“We know we’re not there to make the numbers up.
“It’s a case now of getting back to what Rangers should be winning, targeting what Rangers have done in the past.
“Historically, they’ve been a dominant force in Scottish football. So it’s about us making sure that we give all we can so we can get back to winning top Rangers silverware.”