Tyson joined Blackpool on deadline day, claiming he did not know why he was suddenly not in the first-team picture with the Rams.
But Clough has responded by revealing that he told Tyson at the end of last season what the situation was at the club, and that other strikers would be brought in.
"We had a chat at the end of last season about the situation and told him we were going to bring players in," Clough told the Derby Telegraph.
"Sam Rush (Rams chief executive) was in constant contact, several times a week, with Nathan's dad, who I think works as his representative.
"Nathan did some pre-season with us but he has always known the situation, which is the reason he didn't have a squad number. If you don't get a squad number, then you are struggling."
Tyson joined Derby from rivals Nottingham Forest in June 2011, but has scored just five goals for the Rams - but despite this, Clough insists he has no regrets signing him.
"Not at all, no," said Clough.
"I think he was the best we could get at the time and on a free transfer as well.
"We gave him a three-year deal. A two-year with an option if he plays so many games would have probably been a better deal but, sometimes, you are put into a corner.
"I don't think there were many better free transfers around at the time.
"Nathan started well but got that injury early on against Aston Villa in the final game of pre-season. He came back at Christmas, played very well in that period and got us going.
"The next summer, we brought in Conor Sammon, who went ahead of Nathan.
"Nathan then got one or two knocks, as he tends to. He asked to go out on loan and it did not work out for him at Millwall. Kenny Jackett (then Millwall manager) hardly used him.
"This summer, we signed Chris Martin and Johnny Russell, and Mason Bennett is emerging. So Nathan gradually got knocked down the pecking order.
"He never really had that injury-free run and so we never got an extended look at him, and he didn't manage to establish that consistency we are looking for.
"We felt he had a chance to prove himself. He has played and he got us a few goals, which was good, but when you look at Conor Sammon's injury record last season - I think he was available for 40-odd games - it is quite a contrast."