The Sky Blues took the lead after just four minutes as nobody picked up the Coventry players in the box from a corner kick, which allowed Eastwood to tamely tap the ball under Jamie Ashdown's legs.
It was a woeful error from the re-signed 'keeper, but the defence should burden some of the blame for the goal because of such awful basic set-piece defending.
Pompey piled on some pressure after that early setback with Tommy Smith looking lively on the right side of a three-pronged attack. Steve Cotterill's men kept the ball for long periods of the first half but couldn't muster a meaningful attempt at goal.
It looked like Pompey were running out of ideas towards the end of the first half though, as Aidy Boothroyd set out his side so they would be difficult to break down. Pompey's response was to pump hopeless high balls out of play from defence, which was as ineffective as it sounds.
The second half was even worse than the end of the first as the lack of creativity in the Pompey team showed. Once again, the defence resorted to hoofing long balls for Nugent and Smith to chase but they were incredibly inaccurate and increased the frustration of the travelling support.
Coventry were getting plenty of joy on the break with Matt Ritchie really struggling at left back and that showed when David Bell crossed from the right and Eastwood beat Mokoena in the air to head in his second goal of the game.
Pompey's only meaningful attempt at goal came in stoppage time when Marc Wilson's free kick hit the post and the final whistle blew just minutes later to confirm defeat for Steve Cotterill.
In fact, the biggest cheer from the huge contingent of visiting fans was when John Utaka was subbed off for Pete Gregory, one of only four teenage Pompey substitutes.
The Nigerian was utterly inept and failed to make any effort to run for the ball as he coasted through the game without a care, which was the last straw for the Pompey fans who began chanting "take him off".
To think that Harry Redknapp paid £8.1 million for Utaka's "services" back in 2007, a price that looked worth paying after seeing his incredible goal against Bolton. These days we'd be lucky to get £1 million for him and any prospective buyers would have been put off by his performance today.
I'm trying to take some positives from this game but I'm struggling. Wilson was probably our best player today but that isn't saying much. Ashdown wasn't dominant enough when coming for crosses, Sonko's passing was atrocious whilst the uncreative midfield couldn't open up a solid Coventry outfit.
Nugent ran around a bit but had no impact, Smith faded after a bright first twenty minutes and I've already had my rant about Utaka. Unfortunately, Steve Cotterill couldn't change the game because he didn't have anyone of any pedigree to put on!
It was a terrible start to the new season but I'm not too downhearted about this defeat for two reasons.
Firstly, there are 45 games in this season to go and Steve Cotterill needs time to build a squad and the players need time to gel together, so an opening day defeat to a team who always start well isn't anything to panic about.
Secondly, despite how bad we were, I'm grateful that I still have a club to support after Thursday's High Court ruling. It was a great turnout from around 2,000 visiting fans at the Ricoh and I hope the performance won't have put people off from watching Pompey more often this season.
On a final note, I have heard that a takeover deal for Portsmouth FC could happen next week, but it won't necessarily be Balram Chainrai who takes over. So perhaps there is some good news on the horizon?
Pompey Player Ratings
Jamie Ashdown: 4 - Shocking error for the opener and didn't look confident coming for crosses.
Hayden Mullins: 5 - Should probably have played at left back.
Aaron Mokoena: 5 - Outjumped by Eastwood for second goal.
Ibrahima Sonko: 4 - Looked shaky and his passing was extremely poor.
Matt Ritchie: 4 - Out of position and it certainly showed as Cov's wingers constantly got the better of him.
Marc Wilson: 6 - Showed some ability and drive on the ball, but still rather average.
Michael Brown: 5 - Didn't get in people's faces enough.
Richard Hughes: 5 - Game passed him by.
John Utaka: 3 - Not interested as shown by lack of effort and willingness to take people on.
Tommy Smith: 6 - Was bright at the start, but faded as the game went on.
David Nugent: 5 - Ran a bit but could do nothing with no service.
Substitutes
Liam O'Brien
Peter Gregory (Utaka 83): N/A - Can't have been worse than Utaka.
Marlon Pack
Nadir Ciftci (Hughes 73): N/A - Wasted one cross but didn't do anything else.