Sam Allardyce was relieved but felt England were good value for their win over Slovakia in the first game of his reign.
Adam Lallana's goal, in time added on beyond the scheduled four minutes of stoppage time after lengthy treatment to home goalkeeper Matus Kozacik, earned a 1-0 World Cup qualifying win over a stubborn team who had captain Martin Skrtel sent off.
Allardyce told ITV: "It was a bit nerve-wracking at the end. A 10 men scenario means you must win.
"It's difficult to break them down, they're going to try harder and defend longer but finally we got what we deserved with one in the last minute - perhaps their goalie shouldn't have stayed down injured so long."
It had looked as though the game would end in frustration after Lallana hit a post and Theo Walcott had a goal disallowed for offside.
"Walcott's was definitely a goal, it looked like it came off their defender," said Allardyce, though replays showed a slight touch off Daniel Sturridge.
"In the end we got the goal and it's a deserved win. We broke them down pretty well apart from the final finish. W hen we got the final finish it was offside, we got a goal disallowed when it shouldn't have been, Adam Lallana hit the post and eventually we got the goal."
Lallana said of his decisive contribution: "It's been a long time coming, I put pressure on myself and I knew it was just a matter of time.
"I had a few chances tonight, (the shot against the post) was a great effort.
"We kept plugging away and credit to the lads, it's a great start for Sam and the team. He made it very clear that we needed to keep a clean sheet, anywhere you play away from home it's going to be tough."
Captain Wayne Rooney was again used in a midfield role, as he was for much of England's Euro 2016 disappointment under Roy Hodgson.
The Manchester United man insisted the role "suits me in this team" and Allardyce was happy to give him freedom.
"Today, (he could play) anywhere he wants because he was brilliant," said Allardyce.
"It's one player's position, we won the game. It's a team that plays as team, if it wins it wins, if it loses it gets criticised."
Source: PA
