Recently, network coding has been applied to reliable multicast in wireless networks for packet loss recovery, resulting in significant bandwidth savings. In network-coding-based multicast schemes, once a receiver receives one packet from the source it sends an ACK to acknowledge packet receipt. Such acknowledgment mechanism has the following limitation: when an ACK from one receiver is lost, the source considers the corresponding packet to be lost at this receiver and then conducts unnecessary retransmission. Motivated by this basic observation, we first propose a block-based acknowledgment mechanism, where an ACK now acknowledges all previously received packets in the current block such that the later received ACKs can offset the loss of previous ACKs. To reduce the total amount of feedback overhead, we further propose a more simple feedback mechanism, in which the receivers only start to send acknowledgments from the last two packets (not from the first one as in the first mechanism) of the current block. The first mechanism has the potential to achieve better performance over the latter one in wireless networks with long deep fades (i.e., continuous packet losses) due to its continuous transmissions of ACKs, while the second one is more promising for wireless networks with only random packet losses due to its smaller amount of feedback. Both theoretical and simulation results demonstrate that, compared to the current acknowledgment mechanism in network-coding-based reliable multicast schemes, these two mechanisms can achieve much higher bandwidth efficiency.