First half goals from Febian Brandy and Will Grigg gave the Saddlers their fourth win in five games since going 16 without a win.
Smith said: "I'm proud of the players. We never reached the heights of the last few weeks but on the balance of play I thought we were the better team.
"We looked tired towards the end but we have played five games in 13 days and won four of them, which is a magnificent achievement. We have taken 12 points out of a possible 15 which is not bad at all.
"We were not as fluent as we have been and there were some misplaced passes which gave them hope in the game, but when we got the first goal I think their heads dropped a bit. We have been pretty consistent and it was just a case of getting wins, but since getting 'over the line' against Colchester we have done very well."
Pompey were the better side for the first 20 minutes and Paul Benson missed a great chance to put them in front when he volleyed over in the 19th minute with only the keeper to beat, but Brandy put Walsall in front after 29 minutes from Grigg's headed pass and Grigg got the second five minutes from half time after Grigg made the opening.
David Connolly almost grabbed a goal for the visitors but Karl Darlow saved his rocket shot in the 85th minute.
Caretaker Pompey manager Guy Whittingham said: "Walsall were on a similar run to us and now they have won four out of five, but we need to find almost promotion form.
"Until they scored there was not much in it, but the first goal gave them a lift. It's not funny being on a losing run, but we have to make sure we are doing the right things and take all the positives we can.
"We always knew it was going to be a battle in the situation we are in, but our fans applauded the players off at the end. We lost two goals through silly defensive decisions tonight. We are facing a big task, but you never know."