Neil Lennon insists he still can't believe Giovanni van Bronckhorst was sacked by Rangers earlier this campaign.
And the Celtic hero has warned Michael Beale that it would be "pretty damning" if the Ibrox club went the entire season without winning a trophy.
Rangers take on the Hoops at Hampden this weekend in the semi-finals of the Scottish Cup.
The winners of the tie at the national stadium will then return for the showpiece final event against either Inverness or Falkirk on June 3.
Since Beale was drafted in as van Bronckhorst's replacement in the Ibrox hotseat in November, Rangers have lost twice to Celtic and managed one draw.
Lennon insists the Englishman must find a way to get the better of Ange Postecoglou's side or he risks facing immense pressure heading into the summer transfer window.
He told Boyle Sports: "There are two sides to this. As a Rangers manager, you are judged on what you can do against Celtic; as a Celtic manager, you are judged on how you perform against Rangers.
"So far Michael has a draw and two defeats against Celtic in the three games they have had together. The performances have been better than what they were previously, but you still have to get that win otherwise you come under criticism, scrutiny, and analysis.
"A season without a trophy is pretty damning in Glasgow. He will obviously get a summer transfer window.
"I was also surprised that Giovanni van Bronckhorst was sacked in the first place. He had won the Scottish Cup and qualified for the Champions League. But it was a knee-jerk reaction to the four-nil defeat they suffered at the hands of Celtic earlier in the season.
"I think if Rangers win, they will be facing Inverness or Falkirk in the final, and either Rangers or Celtic will be favourites to win the whole tournament."
Meanwhile, Gordon Strachan has questioned whether Rangers can cope with Celtic's fitness levels.
While Strachan - who won the cup four times as a player and manager in his career - admits there's plenty of talent in Michael Beale's ranks, the pundit remains unconvinced of their fitness levels compared to Celtic.
He said: "There’s plenty of talented players (at Rangers) but do they have the fitness level and the attitude that the team comes first if they don’t play for 90 minutes? That’s the criteria to play for Celtic, so that might be a problem for some (Rangers) players.
"I watched the League Cup Final myself and it was very close like most people thought. But what happened after about 38 minutes was Rangers’ fitness levels went, which allowed Celtic to dominate the last 10 minutes of the half. That shows how important fitness is."
