Goalscorer Nelson said the match was "amazing", despite a slow start, it was a "great" game to play in.
"Couldn't have got gone much better than that for me after coming on. Delighted with the goals and the assist. I have been training for my chance and I got it and tried my best to take it," Nelson said.
"We are just trying to do well for the gaffer and the team. We're top now and it's nice, hopefully we can go all the way."
Nelson had not appeared in the Premier League since August 2021, but took his chance to score his first from a rebound after Dean Henderson had saved his initial shot, and then three minutes later turned in Gabriel Jesus' cross.
England international Saka was forced off injured in the first-half after the midfielder went down after a challenge and tried to continue but came off after 27 minutes.
The injury to Saka will be a major concern for manager Mikel Arteta and his England counterpart Gareth Southgate three weeks ahead of the start of the World Cup in Qatar.
"It is a huge shame for Arsenal and the nation and we will go and check now and see how he is is. He's a great boy and it's great to have him in the team," Nelson said on Saka's injury.
"We found out after the game, it was really bad and unfortunate and some of the lads wished him well on the phone. He is a great guy and we wish him well in his recovery."
With the victory, Arsenal return to the top spot in the table on 31 points with Manchester City two points behind them, while Forest remain bottom on nine points.
Arsenal could have scored more as they wasted numerous opportunities in their ninth Premier League home win in a row, and while Jesus was perhaps the chief culprit, he was excellent in an otherwise lively display, providing two assists.
Information from Reuters contributed to this report.