Rovers' wait for successive victories at league level extends back to March as they failed to follow up Saturday's stunning victory at Sunderland with another milestone win over another of the division's big-hitters.
The only goal of the game arrived on 39 minutes when Tyreeq Bakinson netted from close range on a night when Ipswich were much more dominant than the margin of victory suggested.
Rovers, for their part, showed willingness, effort and fight, but lacked quality on a night when they lost on home soil for the sixth straight game.
They remain eight points from safety, with Gillingham being the only winners in the bottom five. Crewe, Morecambe and AFC Wimbledon all lost, while Fleetwood drew at home.
McSheffrey, who saw Tommy Rowe and Ro-Shaun Williams exit due to injury at the interval, said: "It is a bit of a lifeline, but hugely disappointing as well as we were the only team in the bottom half to take a win on Saturday and we clawed back a few points.
"But at least, we got to grips with how they were playing as there were times in the first half where we hoped we did not concede a second as we have seen it happen.
"I was pleased with how we set up defensively.
"Obviously, we are disappointed to lose the game. I think in terms of how they play, they are probably the best football team who have come here, in terms of their first-half performance and the way they move the ball and the rotations.
"We got to grips with it when we spoke to them at half-time, but sometimes, you want players to work things out on the pitch and it made we have to sit off a bit deeper.
"We defended what they threw at us, but the goal was cheap. At least, make them work for their goal and as good as their play was in all their build-up, we actually defended quite well when they got into our box in the first half. But to give the goal away was disappointing.
"In the second half, we stopped their free-flowing football with our shape. Did we have enough threats on their goal? No.
"I was happy that we did not look a soft easy touch and we handled their wide men who are a real threat. The Ipswich team are a really fit bunch of lads, but we did not cause enough problems in terms of in their penalty box and in behind them.