The pair were voted Leicester's best by supporters using the Tigers App for their performances in the eight-point defeat to Worcester Warriors at Sixways Stadium in the first Gallagher Premiership fixture of the 2019/20 season.
Speaking after the match, the pair echoed one another in their views on both the match and the "bittersweet" fan-voted prize.
"It's a disappointing feeling in the changing rooms at the moment, we felt we could have got something out of today," said Thompson.
"Ultimately, we hurt ourselves at key moments and didn't deliver the performance we know we are capable of and came here to put out.
"The award is nice and I'm grateful to those fans who voted and all those who came out to support us today ... they deserved more."
Thompson's team-mate Hardwick, who was a late inclusion into the starting side after Kyle Eastmond was ruled out through illness ahead of kick-off, said: "I'm feeling the same as Guy, disappointed and feel a bit bittersweet in getting the award after not getting a result."
"We are down now and will keep that feeling to motivate us to try and not feel this way again.
"The performance we put in across the full 80 minutes wasn't up to our standard ... we have to be better and we will be better, starting next Sunday against Sarries at home."