Tait returned from a long-term ankle injury to take his place in the Tigers starting XV at Allianz Park for the first time since last season's Aviva Premiership Final.
And the full-back said Tigers would use the hurt from the 49-10 defeat with back-to-back home games against Sale and Bath on the horizon.
Tait said: “It was a disappointing day. At half-time I thought we were in the mix.
“We played well in the first 40 minutes and with the wind and the conditions were within touching distance.
“It’s difficult to lose two guys to the bin against a quality team like Saracens. It was always going to make it hard.
“The second-half was disappointing. We know we’re better than that. We have to regroup now.
We are very disappointed but after two very good wins in Europe we rested a few bodies. We have two home games and we will players to come back in.
“Everyone is hurting. This will be bottled for next week and when Saracens come to us. We have Sale and Bath and have to win both of those to keep us in the mix.”
Tickets are available now from the Tigers ticket office for the games against Sale Sharks on Saturday, December 28 (3pm) and Bath Rugby on Sunday, January 5 (2pm). Call on 0844 856 1880 or click here.